scholarly journals Using a Toy Model to Improve the Quantization of Gravity and Field Theories

2021 ◽  
Author(s):  
John Klauder
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Positive Result ◽  
Harmonic Oscillator ◽  
Canonical Quantization ◽  
Field Theories ◽  
Quantization Procedure ◽  
Quantization Of Gravity

A half-harmonic oscillator, which gets its name because the coordinate is strictly positive, has been quantized and determined that it was a physically correct quantization. This positive result was found using affine quantization (AQ). The main purpose of this paper is to compare results of this new quantization procedure with those of canonical quantization (CQ). Using Ashtekar-like classical variables and CQ, we quantize the same toy model. While these two quantizations lead to different results, they both would reduce to the same classical Hamiltonian if $\hbar\rightarrow0$. Since these two quantizations have differing results, only one of the quantizations can be physically correct. Two brief sections illustrate how AQ can correctly help quantum gravity and the quantization of most field theory problems.

Conditional interpretation of time in quantum gravity and a time operator in relativistic quantum mechanics

2020 ◽  
Vol 35 (21) ◽  
pp. 2050114
Author(s):  
M. Bauer ◽  
C. A. Aguillón ◽  
G. E. García
Keyword(s):  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Relativistic Quantum ◽  
Canonical Quantization ◽  
Time Operator ◽  
Relativistic Quantum Mechanics ◽  
Problem Of Time ◽  
Quantization Of Gravity ◽  
Dynamical Time ◽  
Spatial Coordinates

The problem of time in the quantization of gravity arises from the fact that time in Schrödinger’s equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus “time” in QM and “time” in general relativity (GR) are seen as mutually incompatible notions. The introduction of a dynamical time operator in relativistic quantum mechanics (RQM), that follows from the canonical quantization of special relativity and that in the Heisenberg picture is also a function of the parameter [Formula: see text] (identified as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of time in the canonical quantization approach to quantum gravity is developed.

TIME AND INTERPRETATIONS OF QUANTUM GRAVITY

2011 ◽  
Vol 20 (supp01) ◽  
pp. 3-86 ◽  
Author(s):  
KAREL V. KUCHAŘ
Keyword(s):  
Quantum Gravity ◽  
Physical Interpretation ◽  
Canonical Quantization ◽  
The State ◽  
Quantization Of Gravity

In canonical quantization of gravity, the state functional does not seem to depend on time. This hampers the physical interpretation of quantum gravity. I critically examine ten major attempts to circumvent this problem and discuss their shortcomings.

Quantum Field Theory

2020 ◽  
pp. 237-288
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Canonical Quantization ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Coordinate Space ◽  
Matrix Formalism ◽  
Quantum Field ◽  
Transfer Matrix Formalism

Chapter 7 covers the main reasons for adopting the methods of quantum field theory (QFT) to study the critical phenomena. It presents both the canonical quantization and the path integral formulation of the field theories as well as the analysis of the perturbation theory. The chapter also covers transfer matrix formalism and the Euclidean aspects of QFT, the field theory of the Ising model, Feynman diagrams, correlation functions in coordinate space, the Minkowski space and the Legendre transformation and vertex functions. Everything in this chapter will be needed sooner or later, since it highlights most of the relevant aspects of quantum field theory.

scholarly journals AN APPLICATION OF NEUTRIX CALCULUS TO QUANTUM FIELD THEORY

2006 ◽  
Vol 21 (02) ◽  
pp. 297-312 ◽  
Author(s):  
Y. JACK NG ◽  
H. VAN DAM
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Effective Field Theories ◽  
Quantum Gravity ◽  
Asymptotic Series ◽  
Effective Field ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Neutrix Calculus

Neutrices are additive groups of negligible functions that do not contain any constants except 0. Their calculus was developed by van der Corput and Hadamard in connection with asymptotic series and divergent integrals. We apply neutrix calculus to quantum field theory, obtaining finite renormalizations in the loop calculations. For renormalizable quantum field theories, we recover all the usual physically observable results. One possible advantage of the neutrix framework is that effective field theories can be accommodated. Quantum gravity theories will then appear to be more manageable.

scholarly journals TIME AND TACHYON

2003 ◽  
Vol 18 (26) ◽  
pp. 4869-4888 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Canonical Quantization ◽  
Recent Analysis ◽  
Late Time ◽  
Classical Dynamics ◽  
One To One ◽  
Definition Of

Recent analysis suggests that the classical dynamics of a tachyon on an unstable D-brane is described by a scalar Born–Infeld type action with a runaway potential. The classical configurations in this theory at late time are in one to one correspondence with the configuration of a system of noninteracting (incoherent), nonrotating dust. We discuss some aspects of canonical quantization of this field theory coupled to gravity, and explore, following an earlier work on this subject, the possibility of using the scalar field (tachyon) as the definition of time in quantum cosmology. At late "time" we can identify a subsector in which the scalar field decouples from gravity and we recover the usual Wheeler–de Witt equation of quantum gravity.

scholarly journals Unitary Issues in Some Higher Derivative Field Theories

Galaxies ◽  
2018 ◽  
Vol 6 (1) ◽  
pp. 23 ◽  
Author(s):  
Manuel Asorey ◽  
Leslaw Rachwal ◽  
Ilya Shapiro
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Gravity ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Higher Derivative

We analyze the unitarity properties of higher derivative quantum field theories which are free of ghosts and ultraviolet singularities. We point out that in spite of the absence of ghosts most of these theories are not unitary. This result confirms the difficulties of finding a consistent quantum field theory of quantum gravity.

scholarly journals Renormalization of Group Field Theories for Quantum Gravity: New Computations and Some Suggestions

2021 ◽  
Vol 8 ◽  
Author(s):  
Marco Finocchiaro ◽  
Daniele Oriti
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Research Area ◽  
Scaling Behavior ◽  
Field Theories ◽  
Numerical Techniques ◽  
Research Directions ◽  
The Status ◽  
Group Field Theory

We discuss motivation and goals of renormalization analyses of group field theory models of simplicial 4d quantum gravity, and review briefly the status of this research area. We present some new computations of perturbative Group field theories amplitudes, concerning in particular their scaling behavior, and the numerical techniques employed to obtain them. Finally, we suggest a number of research directions for further progress.

THE CP PROBLEM IN QUANTUM GRAVITY

1989 ◽  
Vol 04 (06) ◽  
pp. 1493-1514 ◽  
Author(s):  
ABHAY ASHTEKAR ◽  
A.P. BALACHANDRAN ◽  
S. JO
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Canonical Quantization ◽  
Field Theories ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Local Gauge ◽  
Canonical Variables ◽  
Carry Over ◽  
Theories Of Gravitation

It has recently been shown that one can reformulate general relativity in such a way that the canonical variables of the theory resemble those of Yang-Mills theory and the freedom in performing internal rotations on tetrads is completely analogous to the freedom in performing local gauge transformations in Yang-Mills theory. This reformulation is used to carry over, in the canonical framework, the analysis of the θ vacua and the associated CP problem from Yang-Mills theory to general relativity. The analysis depends only on certain qualitative features of general relativity—shared by other field theories of gravitation such as supergravity—and is insensitive to the details of the theory as well as of the way in which the canonical quantization program may be eventually completed.

TELEPARALLELIZED AND AFFINE THEORIES OF GRAVITY: NEW PERSPECTIVES FOR MACHIAN AND QUANTUM GRAVITY

2002 ◽  
Vol 17 (29) ◽  
pp. 4153-4160 ◽  
Author(s):  
HORST-HEINO VON BORZESZKOWSKI
Keyword(s):  
Quantum Gravity ◽  
Canonical Quantization ◽  
Mach's Principle ◽  
Mach’S Principle ◽  
Quantization Of Gravity ◽  
Theories Of Gravity

We compare metric theories to theories with teleparallelism and affine theories of gravity in order to discuss perspectives in the canonical quantization of gravity opened by a realization of Mach's principle.

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.

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