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 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 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 Renormalization Group evolution from on-shell SMEFT

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Minyuan Jiang ◽  
Teng Ma ◽  
Jing Shu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
High Dimensional ◽  
Anomalous Dimensions ◽  
The Standard Model ◽  
Group Evolution

Abstract We describe the on-shell method to derive the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective Field Theory (SMEFT), and exceptionally efficient based on the amplitude basis in hand. The UV divergence is obtained by firstly calculating the coefficients of scalar bubble integrals by unitary cuts, then subtracting the IR divergence in the massless bubbles, which can be easily read from the collinear factors we obtained for the Standard Model fields. Examples of deriving the anomalous dimensions at dimension six are presented in a pedagogical manner. We also give the results of contributions from the dimension-8 H4D4 operators to the running of V+V−H2 operators, as well as the running of B+B−H2D2n from H4D2n+4 for general n.

scholarly journals ON NONLINEARITY OF p-BRANE DYNAMICS

2012 ◽  
Vol 09 (06) ◽  
pp. 1261017 ◽  
Author(s):  
A. A. ZHELTUKHIN
Keyword(s):  
Exact Solutions ◽  
Minkowski Space ◽  
Nonlinear Equations ◽  
New Exact Solutions ◽  
Dimensional Minkowski Space

Nonlinear equations of p-branes in D = (2p + 1)-dimensional Minkowski space are discussed. Presented are new exact solutions for a set of spinning p-branes with the Abelian symmetries U(1) × U(1) × ⋯ ×U(1) of their shapes.

scholarly journals New Representations of Spherical Indicatricies of Bertrand Curves in Minkowski 3-Space

Geometry ◽  
2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
İsmail Aydemir ◽  
Fırat Yerlikaya
Keyword(s):  
Minkowski Space ◽  
3 Dimensional ◽  
Bertrand Curve ◽  
Dimensional Minkowski Space ◽  
Characteristic Features

We obtained a new representation for timelike Bertrand curves and their Bertrand mate in 3-dimensional Minkowski space. By using this representation, we expressed new representations of spherical indicatricies of Bertrand curves and computed their curvatures and torsions. Furthermore in case the indicatricies of a Bertrand curve are slant helices, we investigated some new characteristic features of these curves.

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