Impact Factor 2011 of Journals in Mathematical Physics

New Impact Factor 2011 has been announced.

Impact Factor 2011 of some journals closed to our International Journal of Geometric Methods in Modern Physics by subject and style is the following:

Journal Title	Impact Factor 2011	Impact Factor 2010	Impact Factor 2009	Impact Factor 2008	Impact Factor 2007	5-Year Impact Factor
COMMUN MATH PHYS	1.941	2.000	2.067	2.075	2.070	1.998
LETT MATH PHYS	1.819	0.842	0.969	0.916	1.044	1.223
J PHYS A-MATH THEOR	1.564	1.641	1.577	1.540	1.680	1.344
J MATH PHYS	1.291	1.291	1.318	1.085	1.137	1.181
REV MATH PHYS (WS)	1.213	1.290	1.190	1.258	1.386	1.032
IJGMMP (WS)	0.856	0.757	1.612	1.464	0.662	1.102
J GEOM PHYS	0.818	0.652	0.714	0.683	0.986	0.710
REP MATH PHYS	0.643	0.734	0.658	0.576	0.624	0.627

See Total List of journals in mathematical physics.

Of course, IF essentially depends on a research area. Of course, small journals of < 50 articles in a year have the advantage in IF.

Dmitri Ivanenko's archives: Nobel Laureates Letters

The letters of A. Einstein, L. de Broglie, Ch. Raman, W. Heisenberg, P. A. M. Dirac, A. Sommerfeld, P. Jordan, F. Joliot-Curie, W. Pauli, P. Blackett, H. Yukawa, M. Born, E. Segre, O. Chamberlain, E. Wigner, H. Bethe, H. Alfven, A. Bohr, I. Prigogine, and some other famous scientists are kept in Ivanenko's archives

A. Einstein (Nobel prize in 1921) (a)

L. de Broglie (Nobel prize in 1929) (a, b, c)

Ch. Raman (Nobel prize in 1930) (a)

W. Heisenberg (Nobel prize in 1932) (a, b, c, d, e, f, g, h)

P. A. M. Dirac (Nobel prize in 1933) (a, b, c, d)

F. Joliot-Curie (Nobel prize in 1935) (a)

W. Pauli (Nobel prize in 1945) (a)

P. Blackett (Nobel prize in 1948) (a)

H. Yukawa (Nobel prize in 1949) (a)

M. Born (Nobel prize in 1954) (a)

E. Segre (Nobel prize in 1959) (a)

O. Chamberlain (Nobel prize in 1959) (a)

E. Wigner (Nobel prize in 1963) (a)

H. Bethe (Nobel prize in 1967) (a)

H. Alfven (Nobel prize in 1970) (a)

A. Bohr (Nobel prize in 1975) (a)

I. Prigogine (Nobel prize in 1977) (a)

A. Sommerfeld (a)

P. Jordan (a, b, c, d, e)

J. Wheeler (a, b, c, d)

D. Kerst (a)

H. Pollock (a, b)

F. Reines (a)

E. Amaldi (a)

F. Perrin (a)

V. Weisskopf (a)

W. Panofsky (a)

G. Vataghin (a, b, e)

T. Regge (a)

My book: Generalized Hamiltonian Formalism for Field Theory

Generalized Hamiltonian Formalism for Field Theory

(World Scientific, Singapore, 1995 )

G. SARDANASHVILY

(PDF file)

Preface

Classical field theory utilizes traditionally the language of Lagrangian dynamics.

The Hamiltonian approach to field theory was called into play mainly for canonical quantization of fields by analogy with quantum mechanics. The major goal of

this approach has consisted in establishing simultaneous commutation relations of

quantum fields in models with degenerate Lagrangian densities, e.g., gauge theories.

In classical field theory, the conventional Hamiltonian formalism fails to be so

successful. In the straightforward manner, it takes the form of the instantaneous

Hamiltonian formalism when canonical variables are field functions at a given instant of time. The corresponding phase space is infinite-dimensional. Hamiltonian

dynamics played out on this phase space is far from to be a partner of the usual Lagrangian dynamics of field systems. In particular, there are no Hamilton equations

in the bracket form which would be adequate to Euler-Lagrange field equations.

This book presents the covariant finite-dimensional Hamiltonian machinery for

field theory which has been intensively developed from 70th as both the De Donder

Hamiltonian partner of the higher order Lagrangian formalism in the framework of

the calculus of variations and the multisymplectic (or polysimplectic) generalization

of the conventional Hamiltonian formalism in analytical mechanics when canonical

momenta correspond to derivatives of fields with respect to all world coordinates,

not only time. Each approach goes hand-in-hand with the other. They exemplify

the generalized Hamiltonian dynamics which is not merely a time evolution directed

by the Poisson bracket, but it is governed by partial differential equations where

temporal and spatial coordinates enter on equal footing. Maintaining covariance

has the principal advantages of describing field theories, for any preliminary spacetime splitting shades the covariant picture of field constraints.

Contemporary field models are almost always the constraint ones. In field theory,

if a Lagrangian density is degenerate, the Euler-Lagrange equations are underdetermined and need supplementary conditions which however remain elusive in general. They appear automatically as a part of multimomentum Hamilton equations. Thus, the universal procedure is at hand to canonically analize constraint field systems on the covariant finite-dimensional level. This procedure is applied to a number of

contemporary field models including gauge theory, gravitation theory, spontaneous

symmetry breaking and fermion fields.

In the book, we follow the generally accepted geometric formulation of classical

field theory which is phrased in terms of fibred manifolds and jet spaces.

Contents

1 Geometric Preliminary

1.1 Fibred manifolds

1.2 Jet spaces

1.3 General connections

2 Lagrangian Field Theory

2.1 Lagrangian formalism on fibred manifolds

2.2 De Donder Hamiltonian formalism

2.3 Instantaneous Hamiltonian formalism

3 Multimomentum Hamiltonian Formalism

3.1 Multisymplectic Legendre bundles

3.2 Multimomentum Hamiltonian forms

3.3 Hamilton equations

3.4 Analytical mechanics

3.5 Hamiltonian theory of constraint systems

3.6 Cauchy problem

3.7 Isomultisymplectic structure

4 Hamiltonian Field Theory

4.1 Constraint field systems

4.2 Hamiltonian gauge theory

4.3 Electromagnetic fields

4.4 Proca fields

4.5 Matter fields

4.6 Hamilton equations of General Relativity

4.7 Conservation laws

5 Field Systems on Composite Manifolds

5.1 Geometry of composite manifolds

5.2 Hamiltonian systems on composite manifolds

5.3 Classical Berry’s oscillator

5.4 Higgs fields

5.5 Gauge gravitation theory

5.6 Fermion fields

5.7 Fermion-gravitation complex

Our book in Spanish: D.Ivanenko, G.Sardanashvili, Gravitación

En el libro se expone el punto de vista moderno de la teoría de la gravitación, sus éxitos y dificultades, así como las posibilidades de incorporarla en la teoría unificada de las partículas elementales con ayuda de los modelos gauge y generalizados. Se narra la historia de la creación de la teoría de la relatividad y se exponen sus fundamentos. Se analizan los problemas de los sistemas de referencia, la energía del campo gravitatorio, las singularidades gravitatorias y la cuantificación de la gravitación.
Gravitación (PDF) 

Prólogo a la edición en español
Introducción. Historia y problemas de la teoría de la gravitación
1	Teoría relativista de la gravitación
	1.	El espacio-tiempo de Minkowski
	2.	El espacio-tiempo en la teoría de la gravitación de Einstein
	3.	Fundamentos de la geometría de la TGR
	4.	Las ecuaciones de la teoría de la gravitación
	5.	Catálogo de campos gravitatorios
	6.	Confirmación experimental de la TGR
		Ley de gravitación de Newton
		Principio de equivalencia
		Corrimiento gravitatorio al rojo
		Desviación de la luz debido al Sol
		Precesión de las órbitas planetarias
		Localización láser de la Luna
		Precesión de un giroscopio en una órbita próxima a la Tierra
		Radiolocalización de planetas
		Ondas gravitatorias
2	Enfoques modernos en la teoría de la gravitación
	1.	El principio de relatividad y el problema de los sistemas de referencia
	2.	El principio de equivalencia y la partición (3+ 1)
	3.	El problema de la energía del campo gravitatorio
	4.	Singularidades gravitatorias
	5.	Cosmología moderna
		El problema de la singularidad
		El problema de la homogeneidad y la isotropía
		El problema de la planitud
3	Gravitación y partículas elementales
	1.	Elementos de la teoría de grupos y la tabla de las partículas elementales
	2.	Teoría de los campos gauge y el programa de la Gran Unificación
	3.	Teoría gauge de la gravitación
	4.	Generalizaciones de la TGR. Teoría de la gravitación con torsión
	5.	Gravitación cuántica
		Creación de partículas en un espacio con torsión
		Campo de torsión colectivo
	6.	Superunificación de la gravitación y las partículas elementales
Bibliografía
Índice de autores
Índice de materias

El presente libro está dirigido a estudiantes que apenas se inician en el estudio de la teoría de la gravitación. Su objetivo es dar a conocer al lector las ideas y problemas de la teoría de la gravitación, los cuales, generalmente, no encuentran lugar en los textos de estudio para gravitacionistas principiantes. La mayoría de estos textos de estudio se limita a la teoría general de la relatividad de Einstein y a la geometría seudoriemanniana del espacio-tiempo. En la bibliografía al final del libro se indican al inicio tres colecciones de resúmenes de artículos que cubren muchos de los temas tratados aquí.

La concepción einsteiniana de la gravitación como un campo geometrizado se mantiene en el centro de la atención, ya sea como una teoría no sujeta, según la opinión de muchos autores, a variaciones de ningún tipo, ya sea como uno de los modelos de gravitación más elaborados y consistentes con los experimentos, y sobre cuya base se construyen todas las demás generalizaciones.

Al mismo tiempo, la teoría general de la relatividad de Einstein se encontró con todo un conjunto de problemas internos serios, notados ya desde los tiempos de su creación, pero que han sido encubiertos por los éxitos de la teoría einsteiniana, por lo cual la discusión alrededor de ellos renació sólo en los años 60--70. Se trata del problema de los sistemas de referencia, las dificultades que presenta la búsqueda de una expresión para la energía del campo gravitatorio, de las singularidades gravitatorias y del problema de la geometría de fondo, entre otros. Por ejemplo, ni siquiera está claro cuál es la fuente física del espacio de Minkowski y qué determina la geometría y la topología del espacio en las regiones desiertas entre los cúmulos de galaxias. Los intensos esfuerzos por superar estas dificultades no han tenido éxito hasta el momento, pero han estimulado la búsqueda de nuevos métodos en la teoría de la gravitación, así como el surgimiento de diversos enfoques de revisión, ampliación y generalización de la TGR einsteiniana. A esto se debe agregar que la verificación experimental directa (sin hablar de las observaciones astrofísicas y cosmológicas) se limita por ahora, prácticamente, a la primera aproximación postnewtoniana, dejando grandes posibilidades a los modelos alternativos. En la actualidad nos vemos obligados a hablar no de la teoría, sino de muchas teorías de la gravitación, las cuales conforman un catálogo bastante amplio.

Un motivo importante para el desarrollo y la generalización de la teoría de la gravitación fue siempre la tendencia a establecer la conexión de la gravitación con otras interacciones fundamentales. Estimulado por los éxitos de la física de altas energías, este problema salió a un primer plano. La base reconocida de tal unificación es la teoría gauge. Se han propuesto diferentes modelos gauge de gravitación y en todos ellos la gravitación clásica y la cuántica se describen mediante dos campos geométricos independientes. Estos campos son, al igual que en la TGR, la métrica seudoriemanniana (o campo tetrádico) y la conexión lorentziana, la cual desempeña el papel de potencial gauge de la interacción gravitatoria. Así pues, la geometría de la teoría gauge de la gravitación se encuentra lejos de la sencillez de la geometría seudoriemanniana de la TGR de Einstein, es la geometría afinométrica y la geometría de Klein--Chern de invariantes lorentzianos. En el lenguaje de la teoría gauge, se puede decir que la teoría de la gravitación es una teoría con violación espontánea de las simetrías espaciotemporales, donde la simetría exacta es el grupo de Lorentz. Esta violación espontánea de las simetrías se deduce del principio de equivalencia, y su trasfondo físico es la existencia de materia fermiónica, la cual no admite transformaciones general-covariantes de la arena geométrica, sino, únicamente, transformaciones del grupo de Lorentz. El correspondiente campo de Higgs es el campo gravitatorio geométrico de la TGR. Esto aclara, junto con la naturaleza geométrica de la gravitación, la particularidad de la gravitación como campo físico.

La violación espontánea de la simetría es un fenómeno cuántico condicionado por la existencia de un conjunto de vacíos no-equivalentes. Este fenómeno se simula mediante el campo clásico de Higgs, cuyas características son inherentes también al campo gravitatorio. Una confirmación indirecta de la existencia del vacío de Higgs fue proporcionada por los experimentos de búsqueda de los bosones intermedios, responsables de la interacción electrodébil. Sus masas corresponden a los valores pronosticados por la teoría de Weinberg--Salam. Los campos de Higgs están presentes casi en todos los modelos modernos de las interacciones fundamentales. Estos campos aparecen también en la mayoría de escenarios cosmológicos que describen el estadio inflacionario del Universo temprano. Más aún, los datos de las observaciones cosmológicas se convirtieron en un criterio de elección de unas u otras teorías de unificación de las partículas elementales.

La variedad de modelos de gravitación está acompañada de una variedad de métodos matemáticos, utilizados actualmente en la teoría de la gravitación. Entre ellos se cuentan los espacios fibrados, las variedades de chorros (jet manifolds), la geometría espinorial compleja, las supervariedades, las cuerdas y membranas, la geometría no-conmutativa, etcétera. Es de aceptación general que, precisamente, la geometría diferencial es la que proporciona una formulación adecuada de la teoría de campos clásica, cuando los campos clásicos se describen como secciones de fibrados. De esta manera, al nivel de los campos clásicos, la conocida hipótesis de los años 20 de la posibilidad de una geometrización de todas las interacciones se hizo realidad.

Nobel laureates inscriptions on the walls of Ivanenko's office in Moscow State University

Seven Nobel Laureates: P.A.M. Dirac, H. Yukawa, N.Bohr, I.Prigogine, S.Ting, M. Gell-Mann, G. 't Hooft wrote their famous inscriptions with a chalk on the walls of Ivanenko's office in Moscow State University:

"Physical law should have mathematical beauty" (P.A.M. Dirac, 1956)

"Nature is simple in its essence" (H. Yukawa, 1959)

"Contraria non contradictoria sed complementa sunt" (N.Bohr, 1961)

"Time precedes existence" (I.Prigogine, 1987)

"Physics is an experimental science" (S.Ting, 1988)

"Nature Conformable to Herself in Complexity" (M. Gell-Mann, 2007)

"History repeats itself and will continue to do so, but not in a predictable manner" (G. 't Hooft, 2011)

References: Photo 

My lectures on mathematical physics

G.Sardanashvily, Five lectures on the jet manifold methods in field theory, hep-th/ 9411089

G.Sardanashvily, Ten lectures on jet manifolds in classical and quantum field theory, math-ph/ 0203040

G.Sardanashvily, Fibre bundles, jet manifolds and Lagrangian theory. Lectures for theoreticians, arXiv: 0908.1886v1

G.Sardanashvily, Lectures on supergeometry, arXiv: 0910.0092v1

G.Sardanashvily, Lectures on differential geometry of modules and rings, arXiv: 0910.1515v1

G.Giachetta, L.Mangiarotti, G.Sardanashvily, Advanced mechanics. Mathematical introduction, arXiv: 0911.0411

Lagrangian BRST field theory (from my Scientific biography)

BRST theory emerged in the framework of the quantum theory of gauge fields, where the timing of a degeneration of the Yang - Mills Lagrangian led to its replacement in a generating functional with some modified Lagrangian, depending on ghost fields and invariant under BRST transformations. These BRST transformations resulted from the replacement of parameter functions in gauge transformations with odd ghost fields, and their extension to action on these ghost fields. BRST theory was mainly developed in the framework of Hamiltonian formalism, but its Lagrangian variant also was under consideration. The main works in this direction were the articles of J.Gomis, J.Paris, S.Samuel in 1995 and G.Barnish, F.Brandt, M.Henneaux in 2000 in Physics Reports, as well as preceding works of these authors in the Communication in Mathematical Physics. These works, however, involved the so-called regularity condition which came from BRST theory of Hamiltonian systems with constraints, and which was not appropriate for Noether identities. The latter, in contrast to the algebraic constraint conditions, are the differential identities. Moreover, this BFST theory was developed for fields on .

I was interested in BRST theory, as a kind of prequantum field theory which is a necessary step in the procedure of BV-quantization of fields. Because a BRST operator is nilpotent, I spent the calculation of its relative and iterated cohomology on an arbitrary manifold X [95] in 2000. In 2005, I returned to BRST theory in connection with a consideration of a general type of gauge transformations, depending on the derivatives of fields of arbitrary order [118]. Later, when studying Noether identities, I gave up on the above-mentioned conditions of regularity and introduced a new cohomology condition. In 2008, after constructing a complete description of reducible degenerate Lagrangian systems, I began exploring their BRST extension. Such an extension was proved to be possible if the gauge operator continues to a nilpotent BRST operator acting on ghost fields. In this case, the above-mentioned cochain sequence becomes a complex, called the BRST complex, and an original Lagrangian admits the BRST extension, depending on original fields, antifields, indexing the zero and higher order Noether identities, and ghost fields, parameterizing  zero and higher order gauge symmetries [129]. The BRST extension of some basic field models was built.

References:

 

My Scientific Biography

G.Giachetta, L.Mangiarotti, G.Sardanashvily, Advanced Classical Field Theory  (WS, 2009)

 

Classical mechanics and field theory admit comprehensive geometric formulation

Classical non-relativistic mechanics and classical field theory are adequately formulated in geometric terms of fibre bundles Y->X where dim X>1 in field theory and X=R in mechanics.

Configuration space of a classical non-relativistic mechanics is a fibre bundle Y->R over the time axis R. Its velocity space is a first order jet manifold JY of Y. Its phase space is the vertical tangent bundle VY of Y. Connections on a fibre bundle Y->R characterize non-relativistic reference frames.

Geometric formulation of classical field theory is based on a representation of classical fields by sections of fibre bundles Y->X where dim X>1. Their Lagrangians are densities on finite order jet manifolds of Y.  Connections on Y->X also are fields, e.g., gauge fields which are sections of the first order jet bundle JY->Y. In a very general setting, in order to include odd fields, e.g., fermions  and ghosts, field theory is formulated on a graded manifold whose body is a fibre bundle Y->X.

The formulation of relativistic mechanics generalizes that of non-relativistic mechanics. It is phrased in terms of one-dimensional submanifolds of a configuration space. In a case of two-dimensional submanifolds, we come to classical string theory.

References:

G.Giachetta, L.Mangiarotti, G.Sardanashvily, Advanced Classical Field Theory (WS, 2009)
G.Giachetta, L.Mangiarotti, G.Sardanashvily, Geometric Formulation of Classical and Quantum Mechanics (WS, 2010)
G.Sardanashvily, Fibre bundles, jet manifolds and Lagrangian theory. Lectures for theoreticians, arXiv: 0908.1886
G.Sardanashvily, Advanced mechanics. Mathematical introduction arXiv: 0911.0411

My Library: Completely integrable and superintegrable Hamiltonian systems with noncompact invariant submanifolds

The file Library6.pdf (3Mb) contains the attached PDF files of my main works on generalization of Noether theorems to an arbitrary Lagrangian system  Generalization of the Liouville - Arnold, Nekhoroshev and Mishchenko - Fomenko theorems on action-angle variables of completely integrable, partially integrable and superintegrable Hamiltonian systems to the case of non-compact invariant submanifolds.

Contents

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Action-angle coordinates for time-dependent completely integrable Hamiltonian systems, J. Phys. A 35 (2002) L439-L445

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Geometric quantization of completely integrable Hamiltonian systems in action-angle coordinates, Phys. Lett. A 301 (2002) 53-57

E.Fiorani, G.Giachetta and G.Sardanashvily, Geometric quantization of time-dependent completely integrable Hamiltonian systems, J. Math. Phys. 43 (2002) 5013-5025

E.Fiorani, G.Giachetta and G.Sardanashvily, The Liouville -- Arnold -- Nekhoroshev theorem for non-compact invariant manifolds, J. Phys. A 36 (2003) L101-L107

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Jacobi fields of completely integrable systems, Phys. Lett. A 309 (2003) 382-386

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Bi-Hamiltonian partially integrable systems, J. Math. Phys. 44 (2003) 1984-1987

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Nonadiabatic holonomy operators in classical and quantum completely integrable systems, J. Math. Phys. 45 (2004) 76-86

E.Fiorani and G.Sardanashvily, Noncommutative integrability on noncompact invariant manifolds, J. Phys. A 39 (2006) 14035-14042

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Quantization of noncommutative completely integrable systems, Phys. Lett. A 362 (2007) 138-142

E.Fiorani and G.Sardanashvily, Global action-angle coordinates for completely integrable systems with noncompact invariant submanifolds, J. Math. Phys. 48 (2007) 032901

G.Sardanashvily, Superintegrable Hamiltonian systems with noncompact invariant submanifolds. Kepler system, Int. J. Geom. Methods Mod. Phys. 6 (2009) 1391-1420

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Geometric Formulation of Classical and Quantum Mechanics (World Scientific, Singapore, 2010)

Lagrangian dynamics of higher-dimensional submanifolds

Classical non-relativistic mechanics is adequately formulated as Lagrangian and Hamiltonian theory on a fibre bundle Q-> R over the time axis R, where R is provided with the Cartesian coordinate t possessing the transition functions t'=t+const.  A velocity space of non-relativistic mechanics is the first order jet manifold JQ of sections of Q-> R. Lagrangians of non-relativistic mechanics are defined as densities on JQ. This formulation is extended to time-reparametrized non-relativistic mechanics subject to time-dependent transformations which are bundle automorphisms of Q-> R.

Thus, one can think of non-relativistic mechanics as being particular classical field theory on fibre bundles over X=R. However, an essential difference between non-relativistic mechanics and field theory on fibre bundles Y->X, dim X>1, lies in the fact that connections on Q-> R always are flat. Therefore, they fail to be dynamic variables, but characterize non-relativistic reference frames.

In comparison with non-relativistic mechanics, relativistic mechanics admits transformations of the time depending on other variables, e.g., the Lorentz transformations in Special Relativity on a Minkowski space Q. Therefore, a configuration space Q of relativistic mechanics has no preferable fibration Q-> R, and its velocity space is the first order jet manifold J[1]Q of one-dimensional submanifolds of a configuration space Q. Fibres of the jet bundle J[1]Q-> Q are projective spaces, and one can think of them as being spaces of the three-velocities of a relativistic system. The four-velocities of a relativistic system are represented by elements of the tangent bundle TQ of a configuration space Q.

One can provide a generalization of the above mentioned formulation of relativistic mechanics to the case of submanifolds of arbitrary dimension n. For instance, if n=2, this is the case of classical string theory.

Reference:

G.Sardanashvily, Lagrangian dynamics of submanifolds. Relativistic mechanics arXiv: 1112.0216

A problem of an inertial reference frame in classical mechanics

The key problem of classical mechanics is that there is no intrinsic definition of an inertial reference frame. We have different inertial reference frames which are not inertial with respect to each other.

Classical Lagrangian and Hamiltonian non-relativistic mechanics admits the adequate mathematical formulation in terns of fibre bundle Q->R over the time axis R. In this framework, a reference frame is defined as a trivialization of this fibre bundle or, equivalently, as a connection on Q->R.

A second order dynamic equation is called a free motion equation if it can be brought into the form of a zero acceleration ddq/dtdt=0 with respect to some reference frame,  and this reference frame is said to be inertial for this equation. Thus a definition of an inertial frame depends on the choice of a free motion equation. Given such an equation, different inertial reference frames for this differ from each other in constant velocities.

A problem is that, given a different free motion equation ddq’/dtdt=0, an inertial reference frame for it fails to be so the first free motion equation ddq/dtdt=0, and their relative velocity is not constant.

In view of this problem, one should write dynamic equations of non-relativistic mechanics in terms of relative velocities and accelerations with respect to an arbitrary reference frame. However, in this case the strict mathematical notions of a relative acceleration and a non-inertial force are rather sophisticated.

References:

G.Sardanashvily, Relative non-relativistic mechanics, arXiv: 0708.2998

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Geometric Formulation of Classical and Quantum Mechanics (WS, 2010)

My Library: General Noether theorems

The first and second Noether theorems are formulated in a very general setting of reducible degenerate Lagrangian theories of even and odd variables on fibre bundles and

graded manifolds.

The file Library5.pdf (3 Mb) contains the attached PDF files of my main works on generalization of Noether theorems to an arbitrary Lagrangian system

Contents

G.Sardanashvily, Noether identities of a differential operator. The Koszul--Tate complex, Int. J. Geom. Methods Mod. Phys. 2 (2005) 873-886

D.Bashkirov, G.Giachetta, L.Mangiarotti and G.Sardanashvily, The antifield Koszul--Tate complex of reducible Noether identities, J. Math. Phys. 46 (2005) 103513

D.Bashkirov, G.Giachetta, L.Mangiarotti and G.Sardanashvily, The KT-BRST complex of a degenerate Lagrangian system, Lett. Math. Phys. 83 (2008) 237-252

G.Giachetta, L.Mangiarotti, G.Sardanashvily, On the notion of gauge symmetries of generic Lagrangian field theory, J. Math. Phys. 50 (2009) 012903

G.Sardanashvily, Gauge conservation laws in a general setting: Superpotential, Int. J. Geom. Methods Mod. Phys. 6 (2009) 1047-1056

G.Giachetta, L.Mangiarotti and G.Sardanashvily, Advanced Classical Field Theory  (World Scientific, Singapore, 2009)

On a gauge model of the fifth force

The Poincare group gauge approach which dominated gauge gravitation researches for a long time has not succeeded in providing a gravitational field with the status of a translation gauge potential. Therefore, the question on the physical meaning of this potential arises. At the same time, gauge potentials of spatial translations seem to possess the satisfactory physical utilization for description of dislocations in the theory of continuous media. Based on this result, we have suggested that gauge potentials of Poincare space-time translations can also describe sui generis dislocations of a space-time manifold.

The source of these potentials turns out to be the canonical energy-momentum tensor of matter, and they are inserted into the motion equations of a spinless matter via an effective metric. Therefore, translation gauge fields can contribute to standard gravitational effects. In particular, they may be responsible for an additional exponential (Yukawa) type term to the Newton gravitation potential, i.e., the so-called "fifth force".

This is a hypothetic fifth fundamental interaction which is weaker than gravity. Its experimental verification attracted much attention in 80^th, but nothing was found at least at laboratory distances. However, one discusses the fifth force as possible explanation of the “dark matter” phenomena on the astrophysical and cosmological level.

References