The Conservation Laws and Path-Independent Integrals for Piezo-Magnetic Media

2012 ◽  
Vol 525-526 ◽  
pp. 301-304
Author(s):  
Hai Yan Song ◽  
Jian Sheng Zhou ◽  
Zong Min Liu
Keyword(s):  
Fracture Mechanics ◽  
Conservation Laws ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Important Application ◽  
Analytical Mechanics ◽  
Magnetic Media ◽  
Jacobi Integral

Path-independent integrals have important application value in dislocation, fracture mechanics and other defects theories. Motivated by concepts of Jacobi integral and cyclic integral in analytical mechanics and energy-momentum tensor in electro-magntic field, the conservation laws and path-independent integrals for piezo-magnetic media are derived in this paper.

scholarly journals Quasilocal conservation laws in cosmology: A first look

2020 ◽  
Vol 29 (14) ◽  
pp. 2043029
Author(s):  
Marius Oltean ◽  
Hossein Bazrafshan Moghaddam ◽  
Richard J. Epp
Keyword(s):  
General Relativity ◽  
Cosmological Constant ◽  
Conservation Laws ◽  
Perfect Fluid ◽  
Vacuum Energy ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Stress Energy ◽  
Fluid Matter ◽  
Stress Energy Momentum Tensor

Quasilocal definitions of stress-energy–momentum—that is, in the form of boundary densities (in lieu of local volume densities) — have proven generally very useful in formulating and applying conservation laws in general relativity. In this Essay, we take a basic look into applying these to cosmology, specifically using the Brown–York quasilocal stress-energy–momentum tensor for matter and gravity combined. We compute this tensor and present some simple results for a flat FLRW spacetime with a perfect fluid matter source. We emphasize the importance of the vacuum energy, which is almost universally underappreciated (and usually “subtracted”), and discuss the quasilocal interpretation of the cosmological constant.

FLUIDS IN WEYL GEOMETRIES

2012 ◽  
Vol 09 (02) ◽  
pp. 1260003 ◽  
Author(s):  
L. FATIBENE ◽  
M. FRANCAVIGLIA
Keyword(s):  
Conservation Laws ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Standard Relation ◽  
Number Of Particles

We shall investigate the consequences of non-trivial Weyl geometries on conservation laws of a fluid. In particular we shall obtain a set of properties which allow to obtain in this generalized setting the standard relation between conservation of the energy-momentum tensor and number of particles.

scholarly journals Scrambling with conservation laws

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Gong Cheng ◽  
Brian Swingle
Keyword(s):  
Field Theory ◽  
Conservation Laws ◽  
Energy Momentum Tensor ◽  
Einstein Gravity ◽  
Momentum Tensor ◽  
Late Time ◽  
Current Operator ◽  
Conformal Field ◽  
Time Value ◽  
The Impact

Abstract In this article we discuss the impact of conservation laws, specifically U(1) charge conservation and energy conservation, on scrambling dynamics, especially on the approach to the late time fully scrambled state. As a model, we consider a d + 1 dimensional (d ≥ 2) holographic conformal field theory with Einstein gravity dual. Using the holographic dictionary, we calculate out-of-time-order-correlators (OTOCs) that involve the conserved U(1) current operator or energy-momentum tensor. We show that these OTOCs approach their late time value as a power law in time, with a universal exponent $$ \frac{d}{2} $$ d 2 . We also generalize the result to compute OTOCs between general operators which have overlap with the conserved charges.

scholarly journals CONSERVATION LAWS FOR THE CLASSICAL TODA FIELD THEORIES

1993 ◽  
Vol 08 (35) ◽  
pp. 3377-3385 ◽  
Author(s):  
ERLING G. B. HOHLER ◽  
KÅRE OLAUSSEN
Keyword(s):  
Conservation Laws ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Field Theories ◽  
Conformal Theory ◽  
Infinite Set ◽  
Different Origin

Some explicit calculations of the conservation laws for classical (affine) Toda field theories, and some generlizations of these models are performed. We show that there is a huge class of generalized models which have an infinite set of conservation laws, with their integrated charges being in involution. Amongst these models we find that only the Am, and [Formula: see text] Toda field theories admit such conservation laws for spin-3. The explicit calculations of spin-4 and spin-5 conservation laws in the (affine) Toda models we presented. Our perhaps most interesting finding is that there exist conservation laws in the Am, models (m≥4) which have a different origin than the exponents of the corresponding affine theory or the energy-momentum tensor of a conformal theory.

scholarly journals On the Splitting of the Einstein Field Equations with respect to General (1+3) Threading of Spacetime

2016 ◽  
Vol 2016 ◽  
pp. 1-15
Author(s):  
Aurel Bejancu ◽  
Hani Reda Farran
Keyword(s):  
Conservation Laws ◽  
Perfect Fluid ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Friedmann Equations ◽  
Flrw Universe

Based on general (1+3) threading of the spacetime (M,g), we obtain a new and simple splitting of both the Einstein field equations (EFE) and the conservation laws in (M,g). As an application, we obtain the splitting of EFE in an almost FLRW universe with energy-momentum tensor of a perfect fluid. In particular, we state the perturbation Friedmann equations in an almost FLRW universe.

CASIMIR EFFECT FOR THE ROBIN SURFACES IN STATIC ROBERTSON–WALKER SPACE–TIME

2011 ◽  
Vol 20 (02) ◽  
pp. 161-168 ◽  
Author(s):  
MOHAMMAD R. SETARE ◽  
M. DEHGHANI
Keyword(s):  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Robin Boundary Condition ◽  
Momentum Tensor ◽  
Space Time ◽  
Conformally Invariant ◽  
Time Space ◽  
Robin Boundary

We investigate the energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved surfaces in k = -1 static Robertson–Walker space–time. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Robertson–Walker space–time space is conformally related to Rindler space; as a result we can obtain vacuum expectation values of the energy–momentum tensor for a conformally invariant field in Robertson–Walker space–time space from the corresponding Rindler counterpart by the conformal transformation.

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