Stress-tensor trace anomaly in a gravitational metric: Scalar fields

1977 ◽  
Vol 15 (6) ◽  
pp. 1469-1483 ◽  
Author(s):  
Lowell S. Brown
Keyword(s):  
Stress Tensor ◽  
Scalar Fields ◽  
Trace Anomaly

scholarly journals A note on quantum fields in conformally flat spacetimes

2019 ◽  
Vol 35 (02) ◽  
pp. 1950348
Author(s):  
Swayamsidha Mishra ◽  
Sudipta Mukherji ◽  
Yogesh K. Srivastava
Keyword(s):  
Stress Tensor ◽  
Scalar Fields ◽  
Energy Conditions ◽  
Conformally Flat ◽  
Quantum Fields ◽  
Trace Anomaly ◽  
Flat Spacetimes ◽  
Conformally Flat Spacetimes ◽  
The One ◽  
Spatial Section

We develop a technique relating scalar fields with different masses in different conformally flat spacetimes. We apply this technique to the case of FRW spacetimes, with [Formula: see text], and discuss several examples. We also study various energy conditions and discuss how they constrain the spacetimes related by this technique. We calculate the two-point scalar correlator in the radiation-dominated universe with a hyperbolic spatial section from the one in the Milne universe using the above mapping. Finally, we consider trace anomaly and renormalized stress tensor for conformally flat spacetimes, especially Milne and radiation-dominated universe (with [Formula: see text]) using the transformation.

scholarly journals Quantum fluctuation of stress tensor in a higher-derivative scalar field theory around a cosmic string

2021 ◽  
pp. 2150150
Author(s):  
Nahomi Kan ◽  
Masashi Kuniyasu ◽  
Kiyoshi Shiraishi
Keyword(s):  
Scalar Field ◽  
Stress Tensor ◽  
Cosmic String ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Scalar Fields ◽  
Vacuum Fluctuation ◽  
Higher Derivative ◽  
Scalar Theories ◽  
Quantum Stress Tensor

In this paper, we calculate the vacuum fluctuation of the stress tensor of a higher-derivative theory around a thin cosmic string. To this end, we adopt the method to obtain the stress tensor from the effective action developed by Gibbons et al. By their method, the quantum stress tensor of higher-derivative scalar theories without self-interaction is expressed as a simple sum of quantum stress tensors of free massive scalar fields. Unlike the vacuum expectation value of the scalar field squared obtained in the similar model, there appears no reduction of the values near the conical singularity.

scholarly journals Hadamard’s variational formula in terms of stress and strain tensors

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Björn Gustafsson ◽  
Ahmed Sebbar
Keyword(s):  
Green Function ◽  
Stress Tensor ◽  
Strain Tensor ◽  
Variational Formula ◽  
Scalar Fields ◽  
Action Functional ◽  
Lagrangian Action ◽  
The Green Function ◽  
Strain Tensors ◽  
Hadamard Variational Formula

AbstractStarting from a Lagrangian action functional for two scalar fields we construct, by variational methods, the Laplacian Green function for a bounded domain and an appropriate stress tensor. By a further variation, imposed by a given vector field, we arrive at an interior version of the Hadamard variational formula, previously considered by P. Garabedian. It gives the variation of the Green function in terms of a pairing between the stress tensor and a strain tensor in the interior of the domain, this contrasting the classical Hadamard formula which is expressed as a pure boundary variation.

scholarly journals TRACE ANOMALY AND CASIMIR EFFECT

2000 ◽  
Vol 15 (35) ◽  
pp. 2159-2164 ◽  
Author(s):  
M. R. SETARE ◽  
A. H. REZAEIAN
Keyword(s):  
Boundary Conditions ◽  
Stress Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Casimir Energy ◽  
Two Dimensions ◽  
Dirichlet Boundary Conditions ◽  
Curved Space ◽  
Trace Anomaly ◽  
Dimensional Domain

The Casimir energy for scalar field of two parallel conductors in two-dimensional domain wall background, with Dirichlet boundary conditions, is calculated by making use of general properties of renormalized stress–tensor. We show that vacuum expectation values of stress–tensor contain two terms which come from the boundary conditions and the gravitational background. In two dimensions the minimal coupling reduces to the conformal coupling and stress–tensor can be obtained by the local and nonlocal contributions of the anomalous trace. This work shows that there exists a subtle and deep connection between Casimir effect and trace anomaly in curved space–time.

scholarly journals THE TRACE ANOMALY AND DYNAMICAL VACUUM ENERGY IN COSMOLOGY

2010 ◽  
Vol 25 (11) ◽  
pp. 2391-2408 ◽  
Author(s):  
EMIL MOTTOLA
Keyword(s):  
Effective Action ◽  
Vacuum Energy ◽  
Extreme Ultraviolet ◽  
Planck Scale ◽  
Scalar Fields ◽  
Effective Field ◽  
Massless Scalar ◽  
Energy Tensor ◽  
Theory Approach ◽  
Trace Anomaly

The trace anomaly of conformal matter implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. These poles may be described by a local effective action with massless scalar fields, which couple to classical sources, contribute to gravitational scattering processes, and can have long range gravitational effects at macroscopic scales. In an effective field theory approach, the effective action of the anomaly is an infrared relevant term that should be added to the Einstein-Hilbert action of classical General Relativity to take account of macroscopic quantum effects. The additional scalar degrees of freedom contained in this effective action may be understood as responsible for both the Casimir effect in flat spacetime and large quantum backreaction effects at the horizon scale of cosmological spacetimes. These effects of the trace anomaly imply that the cosmological vacuum energy is dynamical, and its value depends on macroscopic boundary conditions at the cosmological horizon scale, rather than sensitivity to the extreme ultraviolet Planck scale.

scholarly journals Something special at the event horizon

2014 ◽  
Vol 29 (40) ◽  
pp. 1450215 ◽  
Author(s):  
Myungseok Eune ◽  
Yongwan Gim ◽  
Wontae Kim
Keyword(s):  
Black Hole ◽  
Energy Density ◽  
Free Fall ◽  
Scalar Fields ◽  
Negative Energy ◽  
Two Dimensional ◽  
Schwarzschild Black Hole ◽  
Negative Energy Density ◽  
Trace Anomaly ◽  
Physical Consequences

We revisit the free-fall energy density of scalar fields semiclassically by employing the trace anomaly on a two-dimensional Schwarzschild black hole with respect to various black hole states in order to clarify whether something special at the horizon happens or not. For the Boulware state, the energy density at the horizon is always negative divergent, which is independent of initial free-fall positions. However, in the Unruh state the initial free-fall position is responsible for the energy density at the horizon and there is a critical point to determine the sign of the energy density at the horizon. In particular, a huge negative energy density appears when the freely falling observer is dropped just near the horizon. For the Hartle–Hawking state, it may also be positive or negative depending on the initial free-fall position, but it is always finite. Finally, we discuss physical consequences of these calculations.

Stress-tensor trace anomaly in a gravitational metric: General theory, Maxwell field

1977 ◽  
Vol 15 (10) ◽  
pp. 2810-2829 ◽  
Author(s):  
Lowell S. Brown ◽  
James P. Cassidy
Keyword(s):  
General Theory ◽  
Stress Tensor ◽  
Maxwell Field ◽  
Trace Anomaly

Stress tensor and conformal anomalies for massless fields in a Robertson–Walker universe

1977 ◽  
Vol 356 (1687) ◽  
pp. 569-574 ◽  
Keyword(s):  
Stress Tensor ◽  
Scalar Fields ◽  
Casimir Energy ◽  
Massless Scalar ◽  
Einstein Universe ◽  
Massless Fields

We derive the unique, local vacuum stress tensor for electromagnetic, neutrino and massless scalar fields propagating in a Robertson─Walker background spacetime. The result is used to compute the numerical coefficients of the conformal trace anomalies from the known values of the Casimir energy in the Einstein universe.

scholarly journals Verification of Continuum Mechanics Predictions with Experimental Mechanics

Materials ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 77
Author(s):  
Cesar A. Sciammarella ◽  
Luciano Lamberti ◽  
Federico M. Sciammarella
Keyword(s):  
Stress Tensor ◽  
Continuum Mechanics ◽  
Strain Tensor ◽  
Scalar Fields ◽  
Identification Problem ◽  
Theoretical Concept ◽  
Cauchy Stress ◽  
Cauchy Stress Tensor ◽  
Mathematical Functions ◽  
Eulerian Derivative

The general goal of the study is to connect theoretical predictions of continuum mechanics with actual experimental observations that support these predictions. The representative volume element (RVE) bridges the theoretical concept of continuum with the actual discontinuous structure of matter. This paper presents an experimental verification of the RVE concept. Foundations of continuum kinematics as well as mathematical functions relating displacement vectorial fields to the recording of these fields by a light sensor in the form of gray-level scalar fields are reviewed. The Eulerian derivative field tensors are related to the deformation of the continuum: the Euler–Almansi tensor is extracted, and its properties are discussed. The compatibility between the Euler–Almansi tensor and the Cauchy stress tensor is analyzed. In order to verify the concept of the RVE, a multiscale analysis of an Al–SiC composite material is carried out. Furthermore, it is proven that the Euler–Almansi strain tensor and the Cauchy stress tensor are conjugate in the Hill–Mandel sense by solving an identification problem of the constitutive model of urethane rubber.

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