Vacuum polarization energy of a complex scalar field in a vortex background

The Hadamard parametrix is a representation of the short-distance singularity structure of the Feynman Green’s function for a quantum field on a curved spacetime background. Subtracting these divergent terms regularizes the Feynman Green’s function and enables the computation of renormalized expectation values of observables. We study the Hadamard parametrix for a charged, massive, complex scalar field in five spacetime dimensions. Even in Minkowski spacetime, it is not possible to write the Feynman Green’s function for a charged scalar field exactly in closed form. We, therefore, present covariant Taylor series expansions for the biscalars arising in the Hadamard parametrix. On a general spacetime background, we explicitly state the expansion coefficients up to the order required for the computation of the renormalized scalar field current. These coefficients become increasingly lengthy as the order of the expansion increases, so we give the higher-order terms required for the calculation of the renormalized stress-energy tensor in Minkowski spacetime only.

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Universal scaling and echoing in the gravitational collapse of a complex scalar field

Physical Review D ◽

10.1103/physrevd.51.4198 ◽

1995 ◽

Vol 51 (8) ◽

pp. 4198-4207 ◽

Cited By ~ 43

Author(s):

Eric W. Hirschmann ◽

Douglas M. Eardley

Keyword(s):

Scalar Field ◽

Gravitational Collapse ◽

Complex Scalar ◽

Universal Scaling ◽

Complex Scalar Field

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Field models

Introduction to Quantum Field Theory with Applications to Quantum Gravity ◽

10.1093/oso/9780198838319.003.0004 ◽

2021 ◽

pp. 42-69

Author(s):

Iosif L. Buchbinder ◽

Ilya L. Shapiro

Keyword(s):

Electromagnetic Field ◽

Scalar Field ◽

Spinor Field ◽

Vector Fields ◽

Sigma Model ◽

Complex Scalar ◽

Yang Mills ◽

Scalar Field Models ◽

Complex Scalar Field ◽

Mills Field

This chapter provides constructions of Lagrangians for various field models and discusses the basic properties of these models. Concrete examples of field models are constructed, including real and complex scalar field models, the sigma model, spinor field models and models of massless and massive free vector fields. In addition, the chapter discusses various interactions between fields, including the interactions of scalars and spinors with the electromagnetic field. A detailed discussion of the Yang-Mills field is given as well.

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A General Method for Transforming Nonphysical Configurations in BPS States

Advances in High Energy Physics ◽

10.1155/2019/5431067 ◽

2019 ◽

Vol 2019 ◽

pp. 1-11

Author(s):

J. R. L. Santos ◽

A. de Souza Dutra ◽

O. C. Winter ◽

R. A. C. Correa

Keyword(s):

Scalar Field ◽

Condensed Matter ◽

Equations Of Motion ◽

Cosmological Parameters ◽

Topological Defects ◽

Scalar Fields ◽

Complex Scalar ◽

Complex Scalar Field ◽

Bps States ◽

General Method

In this work, we apply the so-called BPS method in order to obtain topological defects for a complex scalar field Lagrangian introduced by Trullinger and Subbaswamy. The BPS approach led us to compute new analytical solutions for this model. In our investigation, we found analytical configurations which satisfy the BPS first-order differential equations but do not obey the equations of motion of the model. Such defects were named nonphysical ones. In order to recover the physical meaning of these defects, we proposed a procedure which can transform them into BPS states of new scalar field models. The new models here founded were applied in the context of hybrid cosmological scenarios, where we derived cosmological parameters compatible with the observed Universe. Such a methodology opens a new window to connect different two scalar fields systems and can be implemented in several distinct applications such as Bloch Branes, Lorentz and Symmetry Breaking Scenarios, Q-Balls, Oscillons, Cosmological Contexts, and Condensed Matter Systems.

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