The God has created a man in order that he creates that the God fails to do

Sunday, 20 April 2014

Gennadi Sardanashvily's Blog Post Archive

List of Sardanashvily’s blog posts (in English)

New ranking: Goggle Scholar Citation

My article: "In memoriam: Dmitri Ivanenko"

Foundations of Modern Physics 12: What are gravitational singularities

57th International Mathematical Olympiad 2016. Results

Our recent article: Partially superintegrable systems on Poisson manifolds

Our recent article: Differential calculus over N-graded commutative rings

Impact Factor 2015

Highly Cited Researchers by countries - 2015

My recent article: Lecture on Gauge Gravitation Theory. Gravity as a Higgs Field

The famous article of V. Ambarzumian and D. Iwanenko in 1930

Ten years of our book "GravitaciĆ³n" (in Spanish)

Foundations of Modern Physics 11: Gauge symmetries

My new book: Noether's Theorems

My recent article: Classical Higgs field

New Lepage Research Institute

Our recent article: Composite bundles in Clifford algebras. Gravitation theory. Part 1

60 Years of Gauge Gravitation Theory

5 Years of our book "Geometric Formulation of Classical and Quantum Mechanics"

Foundations of Modern Physics 10: Relativity Principle

Our new article: Deformation quantization on jet manifolds

10 Years of our book "Geometric and Algebraic Topological Methods in Quantum Mechanics"

Foundations of Modern Physics 9: Gauge gravitation theory

15 Years of our book "Connections in Classical and Quantum Field Theory"

2016 Best Global Universities Rankings

My new article: Noether's first theorem in Hamiltonian mechanics

My philosophical selfie: "Modesty ..."

Who’s who among universities in 2015/16 by THE World University Rankings

20 Years of my book "Generalized Hamiltonian Formalism for Field Theory"

Who is who among universities by QS World University Rankings 2015/16

20th International Summer School on Global Analysis and its Applications

My new article: Inequivalent Vacuum States in Algebraic Quantum Theory

My new article: Higher-stage Noether identities and second Noether theorems

Impact Factor 2014 of journals in Mathematical Physics 

Polysymplectic Hamiltonian field theory

Conference "Geometry of Jets and Fields"

My new "Handbook of Integrable Hamiltonian Systems"

Abstract: Noether theorems in a general setting

Foundations of Modern Physics 8: Relativistic mechanics

World Reputation Rankings 2015 results

My 23 main mathematical theorems

Physicists in favor of and against the atomic bombing of Japan

New book: Introduction to Global Variational Geometry

Special issue of TMP on the 75th birthday of Andrei Slavnov

History of the Universe

Do gravitational waves exist?

The Milky Way map

Recent book on the history of atomic and nuclear physics

 Special issue of TMP on the 80th birthday of Ludvig Faddeev

New article: Classical Higgs fields

Photo: We are scientists

Noether theorems in a general setting

Foundations of Modern Physics 7: Non-relativistic time-dependent mechanics

Who is who among universities in 2014-15 by THE World University Rankings

SUSY gauge theory on graded manifolds

Who is who among universities in 2014

Foundations of modern physics 6: Lagrangian formalism

Archaic human tree

What academic social networks are most popular?

Obituary Prof. Giovanni Giachetta, my colleague and co-author

Impact Factor 2013 of Journals in Mathematical Physics

Foundations of modern physics 5: Supergeometry

Everything on international mathematical Olympiads

It seems that gravitational waves do not exist

Highly cited researchers 2014 by countries

Scientific Biography (#)

My conjecture: gravity is not quantized in general (#)

On a notion of the mathematical structure (#)

Is a metric gravitational field non-quantized? (#)

Geometry of the composite bundles (from my Scientific Biography) (#)

What is Nobel Prize in Physics 2013 for? (#)

Who is who among universities in 2013 by THE World University Rankings (#)

Dmitri Ivanenko and Lev Landau – two archival photos (#)

Who is who among universities in 2013 (#)

Sardanashvily Internet addresses (#)

My lectures on supergeometry (#)

Is supersymmetry illusive? (#)

Solvey Conference 1927: They created contemporary physics (#)

Who is who in modern cosmology theory (#)

How we are small in the Universe (#)

Impact Factor 2012 of Journals in mathematical physics (#)

“Albert Einstein” of Vadim Sidur (#)

My review: “Geometric formulation of non-autonomous mechanics” (#)

Quantum field theory: functional integrals as a true measure (from my Scientific Biography) (#)

Against the Impact Factor (#)

Experiments 2013 look promising … (#)

What is Gauge Gravitation Theory about? (#)

Introduction to my book “Advanced Differential Geometry for Theoreticians” (#)

30 Years of “The Gauge Treatment of Gravity”

What is a classical Higgs field? (#)

Lectures on integrable Hamiltonian systems (#)

My articles in WikipediA (#)

Fibre bundle formulation of time-dependent mechanics (#)

Graded Lagrangian formalism (#)

New Managing Editor of IJGMMP (#)

Any theory is either incomplete or contradictory (#)

Biographic books of WikipediA: Theoretical Physicists, … (#)

Ambarzumyan, Ivanenko and the Sturm – Liouville inverse problem (#)

My favourite painting in the structuralism style (#)

Jet manifold formalism (from my Scientific Biography) (#)

D.Ivanenko’s proton-neutron model of atomic nuclei of 1932 (#)

My review: “Axiomatic quantum field theory” (#)

Different citation indices (#)

My review “Axiomatic classical (prequantum) field theory” (#)

Victor Ambartsumian and Dmitri Ivanenko in history of Quantum Field Theory (#)

My Scientific Biography (#)

Humanity will never leave the Solar system (#)

Introduction to my book “Lectures on Differential Geometry of Modules and Rings”

Infinite-dimensional differential geometry (#)

My new book on differential geometry of modules and rings (#)

Why to gauge gravity? (#)

Discrete space-time (from my Scientific Biography) (#)

What is a mathematical structure? (#)

The Higgs boson or the Higgs vacuum? (#)

Impact Factor 2011 of Journals in Mathematical Physics (#)

Dmitri Ivanenko’s archive: Nobel Laureates Letters (#)

My book: Generalized Hamiltonian Formalism for Field Theory 2012/06/

Our book in Spanish: D.Ivanenko, G.Sardanashvili, GravitaciĆ³n 2012/06/

Nobel laureates inscriptions on the walls of Ivanenko's office in Moscow State University 2012/06/

My lectures on mathematical physics 2012/05/

Lagrangian BRST theory (from my Scientific biografy) 2012/05/

Classical mechanics and field theory admit comprehensive geometric formulation 2012/05/

My Library: Completely integrable and superintegrable Hamiltonian systems with noncompact invariant submanifolds 2012/04/

Lagrangian dynamics of higher-dimensional submanifolds 2012/04/

A problem of an inertial reference frame in classical mechanics 2012/04/

My Library: General Noether theorems 2012/04/

On a gauge model of the fifth force 2012/04/

My Library: Jet Manifold Formalism 2012/03/

Freedom is an immanent property of living nature 2012/03/

Review on our book "Geometric and Algebraic Topological Methods in Quantum Mechanics" in Mathematical Reviews 2012/03/

An energy-momentum is not uniquely deffned 2012/03/

My Library: Time-dependent mechanics 2012/02/

Review on our book "Advanced Classical Field Theory" in Mathematical Reviews 2012/02/

My Library: Advanced Classical Field Theory 2012/02/

My Library: Gauge gravitation theory 2012/02/

Is a momentum space of quantum fields Euclidean? 2012/01/

Hierarchy of Noether identities (from my Scientific Biography) 2012/01/

Can contemporary mathematics describe quantum physics? 2012/01/

Why only electromagnetic and gravitational interactions are in classical physics? 2012/01/

“Antropomorphic” mathematics and the crisis of science 2011/12/

What is a reference frame in field theory and mechanics 2011/12/

Covariant (polysymplectic) Hamiltonian field theory (from my Scientific Biography) 2011/12/

Why a classical system admits different non-equivalent quantization 2011/12/

Five fundamental problems of contemporary physics 2011/11/

Integrable Hamiltonian systems: generalization to a case of non-compact invariant submanifolds (from my Scientific Biography) 2011/11/

On a mathematical hypothesis of quantum space-time 2011/11/

Review on our book “Geometric Formulation of Classical and Quantum mechanics” in Mathematical Reviews 2011/11/

II. How we developed gauge gravitation theory (from my Scientific Biography) 2011/11/

I. How we developed gauge gravitation theory (from my Scientific Biography) 2011/11/

On a mathematical hypothesis of the quark confinement 2011/10/

The prespinor model (from my Scientific Biography 2011/10/

Who is who among Universities in 2011 2011/10/

My Scientific Biography: Student period 2011/10/

Illusion of matter 2011/10/

On the strangeness of relativistic mechanics 2011/09/

”Quantum” causality of ancient Greeks 2011/09/

Why a citation list for a theoretician? 2011/09/

What are classical Higgs fields? 2011/09/

The generalized Serre – Swan theorem is a cornerstone of classical field theory 2011/08/

Metric gravity as a non-quantized Higgs field 2011/08/

What are gauge symmetries? 2011/08/

Why connections in classical field theory? 2011/08/

Geometry in quantum theory IV: Modern geometries 2011/07/

Geometry in quantum theory III: Differential geometry of modules and rings 2011/07/

Does Impact Factor show anything? 2011/07/

Geometry in quantum theory II: Infinite-dimensional fiber bundles 2011/07/

Geometry in quantum theory I: Why familiar differential geometry contributes to quantum theory 2011/07/

Problems of gravitation theory: What is a criterion of gravitational singularities? 2011/06/

On geometric formulation of mechanics 2011/06/

Why connections in field theory 2011/06/

What are general covariant transformations? 2011/06/

What is classical field theory really about? 2011/05/

Non-commutative geometry meets a serious problem 2011/05/

What is meant by supergeometry 2011/05/

Quantum field theory: Functional integrals are not true integrals? 2011/05/

What is a discrete space-time? 2011/05/

What is true Equivalence principle? 2011/04/

On relativistic mechanics in a very general setting 2011/04/

Mechanics as particular classical field theory 2011/04/

What is a fundamental science? 2011/04/

Well-known mathematics that theoreticians do not know 2011/04/

What is true Hamiltonian field theory? 2011/04/

Classical field theory is complete: the strict geometric formulation 2011/03/

My teacher Dmitri Ivanenko, a great theoretician of XX century 2011/03/

50 years of quark star’s idea

At present the hypothesis of quark stars is discussed from different viewpoints, and there are some candidates for quark stars (Wikipedia: Quark star ).

The idea of quark stars has been suggested by D. Ivanenko and D. Kurdgelaidze in 1964. They were motivated both by the hypothesis of a neutron star and the quark model just announced in 1964. At first, Ivanenko and Kurdgelaidze published their quark star model in Soviet journal “Astrophysics1 (1965) 479-481 (in Russian) (#) and then in Lettere al Nuovo Cimento 2 (1969) 13-16 (#).

Tuesday, 8 April 2014

Foundations of Modern Physics 4: Equivalence principle

The Equivalence principle is treated as one of the corner-stones of gravitation theory. However, there exist its different formulations. One separates “weakest”, “weak”, “middle-strong” and “strong” Equivalence principles. All of them are based on the empirical equality of inertial mass, gravitational active and passive charges, and they establish the existence of a certain reference frame, where physical laws would take the known special relativistic form, i. e., a gravitational field effectively disappears.

The “weakest” Equivalence principle is restricted to the motion law of a probe point mass in a uniform gravitational field.

Its sui generis localization is the “weak” Equivalence principle that states the existence of a desired local inertial frame at a given world point. This is the case of equations depending on a gravitational field and its first order derivatives, e. g., the equations of mechanics of probe point masses, and the equations of electromagnetic and Dirac fermion fields.

The “middle-strong” Equivalence principle is concerned with any matter, except a gravitational field, while the “strong” one is applied to all physical laws.

Apparently, only the “weakest” and “weak” Equivalence principles are true. It is the “weak” Equivalence principle that the identification of a gravitational field to a pseudo-Riemannian metric satisfies to.  However, the “weak” Equivalence principle provides a necessary, but not sufficient condition of such identification. Moreover, it does not explain the existence of a gravitational field itself.

To overcome these difficulties, we have reformulated the Equivalence principle as follows.

In geometric terms Special Relativity can be characterized as the geometry of Lorentz invariants. Then the Equivalence principle can be formulated to require the existence of Lorentz invariants on a world manifold X. We agree to call it the geometric Equivalence principle. Its requirement holds if and only if the tangent bundle TX of X admits an atlas with Lorentz transition functions, i. e., a structure group of the associated principal bundle LX of frames in TX is reduced to the Lorentz group SO(1,3). By virtue of the well known theorem, this reduction takes place if and only if the quotient bundle LX/SO(1,3)->X admits a global section, which is a pseudo-Riemannian metric on X.

Thus the geometric Equivalence principle provides the necessary and sufficient conditions of the existence of a pseudo-Riemannian metric on a world manifold that we observe as a gravitational field.

Moreover, if a structure group of the frame bundle LX is reduced to the Lorentz group, it always is reduced to the spatial rotation group SO(3). In accordance with the above mentioned theorem, this reduction defines a space-time decomposition of the tangent bundle TX and, thus, makes a world manifold X into a space-time.

The geometric Equivalence principle also provides the necessary condition of the existence of Dirac’s spinor fields, possessing Lorentz symmetries, on a world manifold.  
Thus, one can think of an observable Dirac fermion matter as being the underlying physical reason of the geometric Equivalence principle and, consequently, the existence of a pseudo-Riemannian gravitational field.

In gravitation theory, the geometric Equivalence principle characterizes spontaneous symmetry breaking of space-time symmetries and, thus, clarifies the physical nature of a gravitational field as a Higgs field responsible for this symmetry breakdown.


D. Ivanenko, G. Sardanashvily, The gauge treatment of gravityPhysics Reports 94 (1983) 1-45.
G. Sardanashvily, Gauge gravitation theory from the geometric viewpoint, Int. J. Geom. Methods Mod. Phys. 3 (2006) N1 v-xx; arXiv: gr-qc/0512115