scholarly journals Field Equations and Lagrangian for the Kaluza Metric Evaluated with Tensor Algebra Software

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
L. L. Williams
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Computer Algebra ◽  
Data File ◽  
The Other ◽  
Tensor Algebra ◽  
Field Equations ◽  
Scalar Field Theory ◽  
Computer Package ◽  
Self Consistency

This paper calculates the Kaluza field equations with the aid of a computer package for tensor algebra, xAct. The xAct file is provided with this paper. We find that Thiry’s field equations are correct, but only under limited circumstances. The full five-dimensional field equations under the cylinder condition are provided here, and we see that most of the other references miss at least some terms from them. We go on to establish the remarkable Kaluza Lagrangian, and verify that the field equations calculated from it match those calculated with xAct, thereby demonstrating self-consistency of these results. Many of these results can be found scattered throughout the literature, and we provide some pointers for historical purposes. But our intent is to provide a definitive exposition of the field equations of the classical, five-dimensional metric ansatz of Kaluza, along with the computer algebra data file to verify them, and then to recover the unique Lagrangian for the theory. In common terms, the Kaluza theory is an “ω=0” scalar field theory, but with unique electrodynamic couplings.

scholarly journals Generic Three-Parameter Wormhole Solution in Einstein-Scalar Field Theory

Particles ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 1-11
Author(s):  
Bobur Turimov ◽  
Ahmadjon Abdujabbarov ◽  
Bobomurat Ahmedov ◽  
Zdeněk Stuchlík
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Exact Analytical Solution ◽  
Naked Singularity ◽  
Radial Coordinate ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Wormhole Solution ◽  
Field Equations ◽  
Scalar Field Theory

An exact analytical, spherically symmetric, three-parametric wormhole solution has been found in the Einstein-scalar field theory, which covers the several well-known wormhole solutions. It is assumed that the scalar field is massless and depends on the radial coordinate only. The relation between the full contraction of the Ricci tensor and Ricci scalar has been found as RαβRαβ=R2. The derivation of the Einstein field equations have been explicitly shown, and the exact analytical solution has been found in terms of the three constants of integration. The several wormhole solutions have been extracted for the specific values of the parameters. In order to explore the physical meaning of the integration constants, the solution has been compared with the previously obtained results. The curvature scalar has been determined for all particular solutions. Finally, it is shown that the general solution describes naked singularity characterized by the mass, the scalar quantity and the throat.

scholarly journals Olbertian Partition Function in Scalar Field Theory

2020 ◽  
Vol 8 ◽  
Author(s):  
R. A. Treumann ◽  
Wolfgang Baumjohann
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Partition Function ◽  
Gaussian Approximation ◽  
Field Equations ◽  
Scalar Field Theory ◽  
Abelian Fields

The Olbertian partition function is reformulated in terms of continuous (Abelian) fields described by the Landau–Ginzburg action, respectively, Hamiltonian. In order to make some progress, the Gaussian approximation to the partition function is transformed into the Olbertian prior to adding the quartic Landau–Ginzburg term in the Hamiltonian. The final result is provided in the form of an expansion suitable for application of diagrammatic techniques once the nature of the field is given, that is, once the field equations are written down such that the interactions can be formulated.

scholarly journals MAPPING A MASSLESS SCALAR FIELD THEORY ON A YANG–MILLS THEORY: CLASSICAL CASE

2009 ◽  
Vol 24 (30) ◽  
pp. 2425-2432 ◽  
Author(s):  
MARCO FRASCA
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
Scalar Field Theory ◽  
Classical Level ◽  
Gradient Expansion ◽  
Yang Mills ◽  
Mills Field

We analyze a recent proposal to map a massless scalar field theory onto a Yang–Mills theory at classical level. It is seen that this mapping exists at a perturbative level when the expansion is a gradient expansion. In this limit the theories share the spectrum, at the leading order, that is the one of a harmonic oscillator. Gradient expansion is exploited maintaining Lorentz covariance by introducing a fifth coordinate and turning the theory to Euclidean space. These expansions give common solutions to scalar and Yang–Mills field equations that are so proved to exist by construction, confirming that the selected components of the Yang–Mills field are indeed an extremum of the corresponding action functional.

scholarly journals Exact Kantowski–Sachs spacetimes in Einstein–Aether scalar field theory

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Genly Leon ◽  
Andronikos Paliathanasis ◽  
N. Dimakis
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Functional Form ◽  
Analytic Solution ◽  
Analytic Solutions ◽  
Field Equations ◽  
Scalar Field Theory ◽  
Gravitational Field Equations ◽  
Background Space ◽  
Gravitational Model

AbstractExact and analytic solutions in Einstein–Aether scalar field theory with Kantowski–Sachs background space are determined. The theory of point symmetries is applied to determine the functional form of the unknown functions which defines the gravitational model. Conservation laws are applied to reduce the order of the field equations and write the analytic solution. Moreover, in order to understand the physical behaviour of the cosmological model a detailed analysis of the asymptotic behaviour for solutions of the gravitational field equations is performed.

scholarly journals Coleman–Weinberg potential in p-adic field theory

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Dmitry S. Ageev ◽  
Andrey A. Bagrov ◽  
Askar A. Iliasov
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Effective Potential ◽  
Space Time ◽  
The Other ◽  
Quantum Corrections ◽  
Real Field ◽  
Scalar Field Theory ◽  
Other Hand ◽  
Peculiar Behavior

AbstractIn this paper, we study $$\lambda \phi ^4$$ λ ϕ 4 scalar field theory defined on the unramified extension of p-adic numbers $${\mathbb {Q}}_{p^n}$$ Q p n . For different “space-time” dimensions n, we compute one-loop quantum corrections to the effective potential. Surprisingly, despite the unusual properties of non-Archimedean geometry, the Coleman–Weinberg potential of p-adic field theory has structure very similar to that of its real cousin. We also study two formal limits of the effective potential, $$p \rightarrow 1$$ p → 1 and $$p \rightarrow \infty $$ p → ∞ . We show that the $$p\rightarrow 1$$ p → 1 limit allows to reconstruct the canonical result for real field theory from the p-adic effective potential and provide an explanation of this fact. On the other hand, in the $$p\rightarrow \infty $$ p → ∞ limit, the theory exhibits very peculiar behavior with emerging logarithmic terms in the effective potential, which has no analogue in real theories.

scholarly journals Scalar field theory limits of bosonic string amplitudes

2000 ◽  
Vol 579 (1-2) ◽  
pp. 379-410 ◽  
Author(s):  
Alberto Frizzo ◽  
Lorenzo Magnea ◽  
Rodolfo Russo
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Bosonic String ◽  
Scalar Field Theory ◽  
String Amplitudes

On causality in polymer scalar field theory

2011 ◽  
Author(s):  
Angel A. García-Chung ◽  
Hugo A. Morales-Técotl ◽  
Luis Arturo Ureña-López ◽  
Hugo Aurelio Morales-Técotl ◽  
Román Linares-Romero ◽  
...  
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Scalar Field Theory

scholarly journals ASYMPTOTIC FREEDOM IN A SCALAR FIELD THEORY ON THE LATTICE

1998 ◽  
Vol 13 (31) ◽  
pp. 2495-2501 ◽  
Author(s):  
KURT LANGFELD ◽  
HUGO REINHARDT
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Scalar Particle ◽  
Higgs Sector ◽  
Asymptotic Freedom ◽  
Scalar Field Theory ◽  
Large N ◽  
The Standard Model ◽  
Conceptual Problems ◽  
The Continuum

A scalar field theory in four space–time dimensions is proposed, which embodies a scalar condensate, but is free of the conceptual problems of standard ϕ4-theory. We propose an N-component, O(N)-symmetric scalar field theory, which is originally defined on the lattice. The scalar lattice model is analytically solved in the large-N limit. The continuum limit is approached via an asymptotically free scaling. The renormalized theory evades triviality, and furthermore gives rise to a dynamically formed mass of the scalar particle. The model might serve as an alternative to the Higgs sector of the standard model, where the quantum level of the standard ϕ4-theory contradicts phenomenology due to triviality.

Sign in / Sign up

Export Citation Format

Share Document