scholarly journals Symplectic Quantization I: Dynamics of Quantum Fluctuations in a Relativistic Field Theory

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Giacomo Gradenigo ◽  
Roberto Livi
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Quantum Fluctuations ◽  
Time Variable ◽  
Quantization Scheme ◽  
Stochastic Quantization ◽  
Relativistic Invariance ◽  
Additional Time ◽  
Relativistic Field ◽  
Time Quantum

AbstractWe propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the action. In this approach the fictitious time of stochastic quantization becomes a genuine additional time variable, with respect to the coordinate time of relativity. This intrinsic time is associated to a symplectic evolution in the action space, which allows one to investigate not only asymptotic, i.e. equilibrium, properties of the theory, but also its non-equilibrium transient evolution. In this paper, which is the first one in a series of two, we introduce a formalism which will be applied to general relativity in its companion work (Gradenigo, Symplectic quantization II: dynamics of space-time quantum fluctuations and the cosmological constant, 2021).

BRST STOCHASTIC QUANTIZATION

1991 ◽  
Vol 06 (28) ◽  
pp. 4985-5015 ◽  
Author(s):  
HELMUTH HÜFFEL
Keyword(s):  
Field Theory ◽  
Particle System ◽  
Relativistic Particle ◽  
Point Particle ◽  
Quantization Scheme ◽  
Stochastic Quantization ◽  
Quantization Method ◽  
Second Quantization ◽  
Spinning Particle ◽  
Constrained Hamiltonian Systems

After a brief review of the BRST formalism and of the Parisi-Wu stochastic-quantization method, the BRST-stochastic-quantization scheme is introduced. This scheme allows the second quantization of constrained Hamiltonian systems in a manifestly gauge-symmetry-preserving way. The examples of the relativistic particle, the spinning particle and the bosonic string are worked out in detail. The paper is closed with a discussion on the interacting field theory associated with the relativistic-point-particle system.

ON STOCHASTIC QUANTIZATION OF WITTEN'S FIELD THEORY OF INTERACTING STRING

1987 ◽  
Vol 02 (10) ◽  
pp. 753-759 ◽  
Author(s):  
YUAN-BEN DAI ◽  
CHUAN-SHENG XIONG ◽  
WEI-DONG ZHAO
Keyword(s):  
Field Theory ◽  
Quantization Scheme ◽  
Stochastic Quantization ◽  
Feynman Rules

Simple Feynman rules are obtained for Witten's theory of interacting string using stochastic quantization scheme.

scholarly journals A new approach to anomalous axial vector field theory

2021 ◽  
pp. 2150104
Author(s):  
A. K. Kapoor
Keyword(s):  
Field Theory ◽  
Axial Vector ◽  
Ultra Violet ◽  
Realistic Model ◽  
Quantization Scheme ◽  
Stochastic Quantization ◽  
Gauge Model ◽  
Operator Formalism ◽  
New Approach ◽  
Vector Gauge

In an earlier paper, it has been shown that the ultra violet divergence structure of anomalous [Formula: see text] axial vector gauge model in the stochastic quantization scheme is different from that in the conventional quantum field theory. Also, it has been shown that the model is expected to be renormalizable. Based on the operator formalism of the stochastic quantization, a new approach to anomalous [Formula: see text] axial vector gauge model is proposed. The operator formalism provides a convenient framework for analysis of ultra violet divergences, but the computations in a realistic model become complicated. In this paper a new approach to do computations in the model is formulated directly in four dimensions. The suggestions put forward here will lead to simplification in the study of applications of the axial vector gauge theory, as well as those of other similar models.

scholarly journals On Hypermomentum in General Relativity II. The Geometry of Spacetime

1976 ◽  
Vol 31 (6) ◽  
pp. 524-527 ◽  
Author(s):  
Friedrich W. Hehl ◽  
G. David Kerlick ◽  
Paul von der Heyde
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Relativistic Field ◽  
Relativistic Field Theory ◽  
General Relativistic ◽  
Dynamical Quantity ◽  
Matter Fields

In Part I** of this series we have introduced the new notion of hypermomentum Δijk as a dynamical quantity characterizing classical matter fields. In Part II, as a preparation for a general relativistic field theory, we look for a geometry of spacetime which will allow for the accomodation of hypermomentum into general relativity. A general linearly connected spacetime with a metric (L4, g) is shown to be the appropriate geometrical framework

scholarly journals Stochastic quantization of axial vector gauge theories with fermions

2019 ◽  
Vol 34 (22) ◽  
pp. 1950176
Author(s):  
A. K. Kapoor
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Gauge Theories ◽  
Axial Vector ◽  
Quantization Scheme ◽  
Quantum Field ◽  
Stochastic Quantization ◽  
Massless Fermion ◽  
Fermion Masses ◽  
Vector Gauge

The stochastic quantization scheme proposed by Parisi and Wu in 1981 is known to have differences from conventional quantum field theory (CQFT) in higher orders. It has been suggested that some of these new features might give rise to a mechanism to explain tiny fermion masses as arising due to radiative corrections. Some features of U(1) axial vector gauge theory in Parisi Wu stochastic quantization are reported. These features are not absent if the theory is formulated in the conventional way. In particular we present arguments for renormalizability of the massive axial vector gauge theory coupled to a massless fermion.

On Hypermomentum in General Relativity I. The Notion of Hypermomentum

1976 ◽  
Vol 31 (2) ◽  
pp. 111-114 ◽  
Author(s):  
Friedrich W. Hehl ◽  
G. David Kerlick ◽  
Paul von der Heyde
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Angular Momentum ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Spin Angular Momentum ◽  
Relativistic Field ◽  
Rank Tensor ◽  
General Relativistic ◽  
Matter Fields

Abstract In this series of notes, we introduce a new quantity into the theory of classical matter fields. Besides the usual energy-momentum tensor, we postulate the existence of a further dynamical attribute of matter, the 3rd rank tensor ⊿ijk of hypermomentum. Subsequently, a general relativistic field theory of energy-momentum and hypermomentum is outlined. In Part I we motivate the need for hypermomentum. We split it into spin angular momentum, the dilatation hypermomentum, and traceless proper hypermomentum and discuss their physical meanings and conservation laws.

WHY MASS APPEARS GRAVITATIONAL

2016 ◽  
pp. 3507-3519
Author(s):  
Mr Casey Ray McMahon
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
The Universe

Einsteins theory of General relativity is a popular theory, but unfortunately it cannot account for all the observable gravity in the universe. This paper presents a new force predicted through the McMahon field theory (2010) [1], which is refered to in McMahon field theory (2010) [1] as Mahona (pronounced “Maa-naa”), which appears to be gravitational. In this paper, I draw upon the McMahon field theory (2010) [1], and use it to explain why mass appears gravitational, as well as the source of the excess gravity that General relativity cannot account for. I will do this in simplistic terms for the benefit of the reader. Thus with the understanding presented here, any vechicle utilising this new force called “Mahona” shall have gravitational capability.

Beyond the Standard Model

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Supergravity Models ◽  
Standard Model ◽  
Field Theories ◽  
Beyond The Standard Model ◽  
Super Symmetry ◽  
The Standard Model ◽  
Topological Field ◽  
Supersymmetric Theories

The motivation for supersymmetry. The algebra, the superspace, and the representations. Field theory models and the non-renormalisation theorems. Spontaneous and explicit breaking of super-symmetry. The generalisation of the Montonen–Olive duality conjecture in supersymmetric theories. The remarkable properties of extended supersymmetric theories. A brief discussion of twisted supersymmetry in connection with topological field theories. Attempts to build a supersymmetric extention of the standard model and its experimental consequences. The property of gauge supersymmetry to include general relativity and the supergravity models.

Introduction

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Gravitational Collapse ◽  
Present State ◽  
Strong Gravity ◽  
Shape Dynamics

Shape Dynamics (SD) is a field theory that describes gravity in a different way than General Relativity (GR): it assumes a preferred notion of simultaneity, and the dynamical content of the theory consists of conformal 3- geometries. SD coincides with (GR) in most situations, in particular in the experimentally well-tested regimes, but it departs from it in some strong-gravity situations, for example at cosmological singularities or upon gravitational collapse. This chapter provides a quick introduction to the theory and a brief description of its present state.

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