scholarly journals Quantum Theory of Massive Yang-Mills Fields. II: Gauge Covariance

1982 ◽  
Vol 67 (4) ◽  
pp. 1206-1215 ◽  
Author(s):  
T. Fukuda ◽  
M. Monda ◽  
M. Takeda ◽  
K.-i. Yokoyama
Keyword(s):  
Quantum Theory ◽  
Yang Mills ◽  
Gauge Covariance

scholarly journals GRAVITY AND YANG–MILLS THEORY

2010 ◽  
Vol 19 (14) ◽  
pp. 2379-2384 ◽  
Author(s):  
SUDARSHAN ANANTH
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Mechanical ◽  
Yang Mills ◽  
Mechanical Description ◽  
Quantum Mechanical Description ◽  
Theory Of Gravity

Three of the four forces of Nature are described by quantum Yang–Mills theories with remarkable precision. The fourth force, gravity, is described classically by the Einstein–Hilbert theory. There appears to be an inherent incompatibility between quantum mechanics and the Einstein–Hilbert theory which prevents us from developing a consistent quantum theory of gravity. The Einstein–Hilbert theory is therefore believed to differ greatly from Yang–Mills theory (which does have a sensible quantum mechanical description). It is therefore very surprising that these two theories actually share close perturbative ties. This essay focuses on these ties between Yang–Mills theory and the Einstein–Hilbert theory. We discuss the origin of these ties and their implications for a quantum theory of gravity.

scholarly journals A COMPARISON OF THE PROPER-TIME EQUATION AND THE RENORMALIZATION GROUP β-FUNCTION IN STRING THEORY

1995 ◽  
Vol 10 (21) ◽  
pp. 1565-1575
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Proper Time ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
The Other ◽  
Proportionality Factor ◽  
Yang Mills ◽  
Higher Covariant Derivative ◽  
Full Equation ◽  
Gauge Covariance ◽  
Β Function

It is known that there is a proportionality factor relating the β-function and the equations of motion viz. the Zamolodchikov metric. Usually this factor has to be obtained by other methods. The proper-time equation, on the other hand, is the full equation of motion. We explain the reasons for this and illustrate it by calculating corrections to Maxwell’s equation. The corrections are calculated to cubic order in the field strength, but are exact to all orders in derivatives. We also test the gauge covariance of the proper-time method by calculating higher (covariant) derivative corrections to the Yang-Mills equation.

scholarly journals Quantum Theory of Massive Yang-Mills Fields. I: Basis of Formulation with Indefinite Metric

1981 ◽  
Vol 66 (5) ◽  
pp. 1827-1842 ◽  
Author(s):  
T. Fukuda ◽  
M. Monda ◽  
M. Takeda ◽  
K.-i. Yokoyama
Keyword(s):  
Quantum Theory ◽  
Indefinite Metric ◽  
Yang Mills

scholarly journals Trace dynamics, and a ground state in spontaneous quantum gravity

2020 ◽  
pp. 2150019
Author(s):  
Abhinash Kumar Roy ◽  
Anmol Sahu ◽  
Tejinder P. Singh
Keyword(s):  
Quantum Theory ◽  
Quantum Gravity ◽  
Ground State ◽  
Quantum Cosmology ◽  
Planck Scale ◽  
Yang Mills ◽  
Energy Eigenvalues ◽  
Initial Epoch ◽  
Unitary Transformations ◽  
The Standard Model

We have recently proposed a Lagrangian in trace dynamics to describe a possible unification of gravity, Yang–Mills fields, and fermions, at the Planck scale. This Lagrangian for the unified entity — called the aikyon — is invariant under global unitary transformations, and as a result possesses a novel conserved charge, known as the Adler–Millard charge. In this paper, we derive an eigenvalue equation, analogous to the time-independent Schrödinger equation, for the Hamiltonian of the theory. We show that in the emergent quantum theory, the energy eigenvalues of the aikyon are characterized in terms of a fundamental frequency times Planck’s constant. The eigenvalues of this equation can, in principle, determine the values of the parameters of the standard model. We also report a ground state, in this theory of spontaneous quantum gravity, which could characterize a non-singular initial epoch in quantum cosmology.

scholarly journals Classical instanton solutions in quantum field theory

2020 ◽  
pp. 78-85
Author(s):  
Roman G. Shulyakovsky ◽  
Alexander S. Gribowsky ◽  
Alexander S. Garkun ◽  
Maxim N. Nevmerzhitsky ◽  
Alexei O. Shaplov ◽  
...  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Yukawa Potential ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Quantum Field ◽  
Two Dimensional ◽  
Yang Mills ◽  
The One

Instantons are non-trivial solutions of classical Euclidean equations of motion with a finite action. They provide stationary phase points in the path integral for tunnel amplitude between two topologically distinct vacua. It make them useful in many applications of quantum theory, especially for describing the wave function of systems with a degenerate vacua in the framework of the path integrals formalism. Our goal is to introduce the current situation about research on instantons and prepare for experiments. In this paper we give a review of instanton effects in quantum theory. We find in stanton solutions in some quantum mechanical problems, namely, in the problems of the one-dimensional motion of a particle in two-well and periodic potentials. We describe known instantons in quantum field theory that arise, in particular, in the two-dimensional Abelian Higgs model and in SU(2) Yang – Mills gauge fields. We find instanton solutions of two-dimensional scalar field models with sine-Gordon and double-well potentials in a limited spatial volume. We show that accounting of instantons significantly changes the form of the Yukawa potential for the sine-Gordon model in two dimensions.

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