scholarly journals Canonical Description for Formulation of Embedding Gravity as a Field Theory in a Flat Spacetime

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 722
Author(s):  
Sergey Paston ◽  
Elizaveta Semenova ◽  
Anton Sheykin
Keyword(s):  
Field Theory ◽  
Minkowski Space ◽  
Path Integral ◽  
Canonical Formalism ◽  
Scalar Fields ◽  
Flat Space ◽  
Implicit Function ◽  
Higher Dimension ◽  
Flat Spacetime ◽  
Canonical Variables

We consider the approach to gravity in which four-dimensional curved spacetime is represented by a surface in a flat Minkowski space of higher dimension. After a short overview of the ideas and results of such an approach we concentrate on the study of the so-called splitting gravity, a form of this description in which constant value surface of a set of scalar fields in the ambient flat space-time defines the embedded surface. We construct a form of action which is invariant w.r.t. all symmetries of this theory. We construct the canonical formalism for splitting gravity. The resulting theory turns out to be free of constraints. However, the Hamiltonian of this theory is an implicit function of canonical variables. Finally, we discuss the path integral quantization of such a theory.

scholarly journals Friedmann cosmology in Regge-Teitelboim gravity

2016 ◽  
Vol 41 ◽  
pp. 1660128 ◽  
Author(s):  
A. A. Sheykin ◽  
S. A. Paston
Keyword(s):  
Field Theory ◽  
Minkowski Space ◽  
Scalar Fields ◽  
Ambient Space ◽  
High Dimensional ◽  
Friedmann Universe ◽  
Quantization Procedure ◽  
Original Theory ◽  
Dimensional Minkowski Space ◽  
Embedded Surfaces

This paper is devoted to the approach to gravity as a theory of a surface embedded in a flat ambient space. After the brief review of the properties of original theory by Regge and Teitelboim we concentrate on its field-theoretic reformulation, which we call splitting theory. In this theory embedded surfaces are defined through the constant value surfaces of some set of scalar fields in high-dimensional Minkowski space. We obtain an exact expressions for this scalar fields in the case of Friedmann universe. We also discuss the features of quantization procedure for this field theory.

scholarly journals Path integral representation for polymer quantized scalar fields

2015 ◽  
Vol 30 (34) ◽  
pp. 1550204 ◽  
Author(s):  
Nirmalya Kajuri
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Integral Representation ◽  
Path Integral ◽  
Loop Quantum Gravity ◽  
Scalar Fields ◽  
Independent Manner ◽  
Path Integral Representation ◽  
Crucial Difference ◽  
Matter Fields

According to loop quantum gravity, matter fields must be quantized in a background-independent manner. For scalar fields, such a background-independent quantization is called polymer quantization and is inequivalent to the standard Schrödinger quantization. It is therefore important to obtain predictions from the polymer quantized scalar field theory and compare with the standard results. As a step towards this, we develop a path integral representation for the polymer quantized scalar field. We notice several crucial differences from the path integral for the Schrödinger quantized scalar field. One important difference is the appearance of an extra summation at each point in the path integral for the polymer quantized theory. A second crucial difference is the loss of manifest Lorentz symmetry for a polymer quantized theory on Minkowski space.

scholarly journals A note on commutation relation in conformal field theory

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Lento Nagano ◽  
Seiji Terashima
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Minkowski Space ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Scalar Fields ◽  
Expectation Value ◽  
Conformal Field ◽  
Free Scalar ◽  
Distance Limit

Abstract In this note, we explicitly compute the vacuum expectation value of the commutator of scalar fields in a d-dimensional conformal field theory on the cylinder. We find from explicit calculations that we need smearing not only in space but also in time to have finite commutators except for those of free scalar operators. Thus the equal time commutators of the scalar fields are not well-defined for a non-free conformal field theory, even if which is defined from the Lagrangian. We also have the commutator for a conformal field theory on Minkowski space, instead of the cylinder, by taking the small distance limit. For the conformal field theory on Minkowski space, the above statements are also applied.

scholarly journals Bra-ket wormholes in gravitationally prepared states

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Yiming Chen ◽  
Victor Gorbenko ◽  
Juan Maldacena
Keyword(s):  
Hyperbolic Space ◽  
Path Integral ◽  
Flat Space ◽  
Low Energy ◽  
Two Dimensional ◽  
De Sitter ◽  
Euclidean Case ◽  
Fine Grained ◽  
Entropy Formula ◽  
First Case

Abstract We consider two dimensional CFT states that are produced by a gravitational path integral.As a first case, we consider a state produced by Euclidean AdS2 evolution followed by flat space evolution. We use the fine grained entropy formula to explore the nature of the state. We find that the naive hyperbolic space geometry leads to a paradox. This is solved if we include a geometry that connects the bra with the ket, a bra-ket wormhole. The semiclassical Lorentzian interpretation leads to CFT state entangled with an expanding and collapsing Friedmann cosmology.As a second case, we consider a state produced by Lorentzian dS2 evolution, again followed by flat space evolution. The most naive geometry also leads to a similar paradox. We explore several possible bra-ket wormholes. The most obvious one leads to a badly divergent temperature. The most promising one also leads to a divergent temperature but by making a projection onto low energy states we find that it has features that look similar to the previous Euclidean case. In particular, the maximum entropy of an interval in the future is set by the de Sitter entropy.

scholarly journals Chiral correlators in $$ \mathcal{N} $$ = 2 superconformal quivers

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Francesco Galvagno ◽  
Michelangelo Preti
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Flat Space ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
Yang Mills ◽  
The Matrix ◽  
Superspace Formalism ◽  
Model Approach

Abstract We consider a family of $$ \mathcal{N} $$ N = 2 superconformal field theories in four dimensions, defined as ℤq orbifolds of $$ \mathcal{N} $$ N = 4 Super Yang-Mills theory. We compute the chiral/anti-chiral correlation functions at a perturbative level, using both the matrix model approach arising from supersymmetric localisation on the four-sphere and explicit field theory calculations on the flat space using the $$ \mathcal{N} $$ N = 1 superspace formalism. We implement a highly efficient algorithm to produce a large number of results for finite values of N , exploiting the symmetries of the quiver to reduce the complexity of the mixing between the operators. Finally the interplay with the field theory calculations allows to isolate special observables which deviate from $$ \mathcal{N} $$ N = 4 only at high orders in perturbation theory.

scholarly journals AN ALGORITHMIC APPROACH TO QUANTUM FIELD THEORY

2006 ◽  
Vol 21 (03) ◽  
pp. 405-447 ◽  
Author(s):  
MASSIMO DI PIERRO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Path Integral ◽  
Gauge Theories ◽  
Quantum Field ◽  
Algorithmic Approach ◽  
Main Emphasis ◽  
Lattice Computation ◽  
Theoretical Foundations ◽  
Minimal Residual

The lattice formulation provides a way to regularize, define and compute the Path Integral in a Quantum Field Theory. In this paper, we review the theoretical foundations and the most basic algorithms required to implement a typical lattice computation, including the Metropolis, the Gibbs sampling, the Minimal Residual, and the Stabilized Biconjugate inverters. The main emphasis is on gauge theories with fermions such as QCD. We also provide examples of typical results from lattice QCD computations for quantities of phenomenological interest.

On Conformally Covariant Spinor Field Equations

1972 ◽  
Vol 50 (18) ◽  
pp. 2100-2104 ◽  
Author(s):  
Mark S. Drew
Keyword(s):  
Minkowski Space ◽  
Invariant Mass ◽  
Spinor Field ◽  
Dimensional Space ◽  
Flat Space ◽  
Field Equations ◽  
First Order ◽  
Conformally Invariant ◽  
Spinor Fields

Conformally covariant equations for free spinor fields are determined uniquely by carrying out a descent to Minkowski space from the most general first-order rotationally covariant spinor equations in a six-dimensional flat space. It is found that the introduction of the concept of the "conformally invariant mass" is not possible for spinor fields even if the fields are defined not only on the null hyperquadric but over the entire manifold of coordinates in six-dimensional space.

The Origin and Bifurcation of Disclinations in the Gauge Field Theory of Dislocation and Disclination Continuum

1998 ◽  
Vol 12 (25) ◽  
pp. 2599-2617 ◽  
Author(s):  
Guo-Hong Yang ◽  
Yishi Duan
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Implicit Function Theorem ◽  
Taylor Expansion ◽  
Gauge Field Theory ◽  
Implicit Function ◽  
Quantum Numbers ◽  
Topological Quantum ◽  
Topological Current ◽  
Limit Points

In the 4-dimensional gauge field theory of dislocation and disclination continuum, the topological current structure and the topological quantization of disclinations are approached. Using the implicit function theorem and Taylor expansion, the origin and bifurcation theories of disclinations are detailed in the neighborhoods of limit points and bifurcation points, respectively. The branch solutions at the limit points and the different directions of all branch curves at 1-order and 2-order degenerated points are calculated. It is pointed out that an original disclination point can split into four disclinations at one time at most. Since the disclination current is identically conserved, the total topological quantum numbers of these branched disclinations will remain constant during their origin and bifurcation processes. Furthermore, one can see the fact that the origin and bifurcation of disclinations are not gradual changes but sudden changes. As some applications of the proposal theory, two examples are presented in the paper.

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