scholarly journals The impulse-energy tensor of material particles

1944 ◽  
Vol 182 (990) ◽  
pp. 302-318
Keyword(s):  
Electromagnetic Field ◽  
Momentum Density ◽  
Momentum Operator ◽  
General Construction ◽  
Energy Tensor ◽  
Gauge Invariant ◽  
Invariant Tensor ◽  
Derivatives Of

The following is a direct and general construction, from the field quantities of the electrons and mesons and their derivatives, of a real, symmetrical and gauge-invariant tensor T kl whose divergence to l is — 1 times the four-force f k experienced by the matter. Interpreting T kl as the impulse-energy tensor of the material particles, for the case of no electromagnetic field the energy-momentum density obtained from T k4 is compared with that obtained from treating (ℏ/ i ) (∂/∂x k ) as the energy-momentum operator. Further, in the general case the Hamiltonian of the matter is compared with ∫ T 44 dxdydz . Both times, the two quantities compared agree apart from small modifications.

scholarly journals Simulation of a rotating strong gravity that reverses time

2021 ◽  
pp. 7-16
Author(s):  
Yoshio Matsuki ◽  
Petro Bidyuk
Keyword(s):  
Angular Momentum ◽  
Gravitational Field ◽  
Momentum Density ◽  
Polar Coordinates ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Strong Gravity ◽  
The Past ◽  
Stress Energy ◽  
The Future

In this research we simulated how time can be reversed with a rotating strong gravity. At first, we assumed that the time and the space can be distorted with the presence of a strong gravity, and then we calculated the angular momentum density of the rotating gravitational field. For this simulation we used Einstein’s field equation with spherical polar coordinates and the Euler’s transformation matrix to simulate the rotation. We also assumed that the stress-energy tensor that is placed at the end of the strong gravitational field reflects the intensities of the angular momentum, which is the normal (perpendicular) vector to the rotating axis. The result of the simulation shows that the angular momentum of the rotating strong gravity changes its directions from plus (the future) to minus (the past) and from minus (the past) to plus (the future), depending on the frequency of the rotation.

scholarly journals CONSTRAINT ALGEBRAS IN GAUGE-INVARIANT SYSTEMS

1995 ◽  
Vol 10 (28) ◽  
pp. 4087-4105 ◽  
Author(s):  
KH. S. NIROV
Keyword(s):  
Wide Class ◽  
Arbitrary Function ◽  
Arbitrary Order ◽  
Local Symmetry ◽  
Poisson Brackets ◽  
Hamiltonian Description ◽  
Gauge Invariant ◽  
Symmetry Transformations ◽  
Constraint Algebra ◽  
Derivatives Of

A Hamiltonian description is constructed for a wide class of mechanical systems having local symmetry transformations depending on time derivatives of the gauge parameters of arbitrary order. The Poisson brackets of the Hamiltonian and constraints with each other and with an arbitrary function are explicitly obtained. The constraint algebra is proved to be of the first class.

The interaction of molecular multipoles with the electromagnetic field in the canonical formulation of non-covariant quantum electrodynamics

1970 ◽  
Vol 319 (1539) ◽  
pp. 549-563 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Physical Interpretation ◽  
Quantum Electrodynamics ◽  
Unitary Transformation ◽  
Canonical Quantization ◽  
Multipole Moments ◽  
Gauge Invariant ◽  
Covariant Quantum ◽  
Canonical Formulation ◽  
Gauge Conditions

The procedure devised by Dirac for the canonical quantization of systems described by degenerate lagrangians is used to construct the hamiltonian for molecules interacting with the electromagnetic field. The hamiltonian obtained is expressed in terms of the gauge invariant field strengths and the electric and magnetic multipole moments of the molecules. The Coulomb gauge is introduced but other gauge conditions could be used. Finally, a physical interpretation of the unitary transformation that may be used to generate the multipole hamiltonian is given.

scholarly journals Derivative expansion for the one-loop effective Lagrangian in QED

1996 ◽  
Vol 74 (5-6) ◽  
pp. 282-289 ◽  
Author(s):  
V. P. Gusynin ◽  
I. A. Shovkovy
Keyword(s):  
Electromagnetic Field ◽  
Field Strength ◽  
External Field ◽  
Explicit Expression ◽  
Derivative Expansion ◽  
Effective Lagrangian ◽  
Constant Electromagnetic Field ◽  
The One ◽  
Derivatives Of

The derivative expansion of the one-loop effective Lagrangian in QED4 is considered. The first term in such an expansion is the famous Schwinger result for a constant electromagnetic field. In this paper we give an explicit expression for the next term containing two derivatives of the field strength Fμν. The results are presented for both fermion and scalar electrodynamics. Some possible applications of an inhomogeneous external field are pointed out.

Electron Momentum Density In Europium Using A 137Cs Compton Spectrometer

2005 ◽  
Vol 60 (7) ◽  
pp. 512-516
Author(s):  
Babu Lal Ahuja ◽  
Harsh Malhotra ◽  
Sonal Mathur
Keyword(s):  
Experimental Data ◽  
Band Structure ◽  
Gamma Rays ◽  
Free Electron ◽  
Cohesive Energy ◽  
Momentum Density ◽  
Compton Profile ◽  
Electron Momentum ◽  
Electron Models ◽  
Derivatives Of

The isotropic Compton profile of europium, the most reactive lanthanide, has been measured at a resolution of 0.40 a.u. using 661.65 keV gamma-rays. In the absence of a band structure-based Compton profile, the experimental data are compared with renormalised-free-atom (RFA) and free electron models. It is seen that the RFA model with e−-e− correlation agrees better with the experiment than the free electron models. The first derivatives of the Compton profiles show the hybridization effects of s-, p-, d-, f-electrons. From our RFA data we have also computed the cohesive energy of europium. PACS: 13.60.F, 71.15.Nc, 78.70. -g, 78.70.Ck

Convective variational approach to relativistic thermodynamics of dissipative fluids

1991 ◽  
Vol 433 (1887) ◽  
pp. 45-62 ◽  
Keyword(s):  
Traditional Approach ◽  
Chemical Constituents ◽  
Momentum Density ◽  
Energy Tensor ◽  
Cauchy Type ◽  
Entropy Current ◽  
Master Function ◽  
Relativistic Thermodynamic ◽  
Set Up ◽  
Generalized Variation

Using guidelines provided by Noether identities arising from a generalized variation procedure of convective type, a new (nonlinear and exactly self-consistent) category of relativistic thermodynamic models is developed for the systematic representation of viscous conducting fluid media (allowing for several independent charged or neutral chemical constituents). Apart from the provision of a set of dissipation coefficients of the usual (reactivity, resistivity, and viscosity) type, the specification of a particular model is determined just by giving the algebraic dependence a single ‘master function’, ͘ Λ say, on the relevant dynamical variables, which are supposed here to consist of an entropy current 4-vector and a set of particle current 4-vectors corresponding to the various chemical constituents, together with a set of symmetric (rank 3) viscosity tensors, which are considered as being dynamically independent of the corresponding current vectors except in the degenerate limit of linear viscosity. The master function is set up as a generalization of an ordinary lagrangian function, to which it reduces in the relevant non - dissipative limit, and, as in the conservative case, it is used for the construction of derived quantities in such a way that appropriate self-consistency conditions are satisfied as identities. In particular the relevant stress-momentum-energy tensor is obtained directly in terms of the independent variables and of their dynamical conjugates (whose role is hidden in the traditional approach as developed by Israel & Stewart), which are set of ordinary 4-momentum (not 4-momentum density) covectors associated with the independent currents, and a set of generalised Cauchy type strain (not strain - rate) tensors associated with the independent viscous stress contributions. The range of application of the category obtained in this way is intended to include that of the standard (Israel-Stewart) formalism to which it is expected to be effectively equivalent in the limit of sufficiently small deviations from thermodynamic equilibrium.

scholarly journals On the flat spacetime Galileons and the Born–Infeld type structures

2015 ◽  
Vol 24 (06) ◽  
pp. 1550041
Author(s):  
Cuauhtemoc Campuzano ◽  
Rubén Cordero ◽  
Miguel Cruz ◽  
Efraín Rojas
Keyword(s):  
Scalar Field ◽  
Variational Analysis ◽  
Momentum Density ◽  
Type Structure ◽  
Field Theories ◽  
Flat Spacetime ◽  
Arbitrary Dimensions ◽  
Derivatives Of ◽  
Galileon Field

We show how the flat spacetime Galileon field theories (FSGFT) in arbitrary dimensions can be obtained through a Born–Infeld (BI) type structure. This construction involves a brane metric and nonlinear combinations of derivatives of a scalar field. Our setup gives rise to some Galileon tensors and vectors useful for the variational analysis which are related to the momentum density of the probe Lovelock branes floating in a N-dimensional flat bulk. We find further that the Noether currents associated to these Galileon theories may be written in terms of such tensors.

Classical electrodynamics of spinning particles

1984 ◽  
Vol 62 (10) ◽  
pp. 943-947
Author(s):  
Bruce Hoeneisen
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Wave Equations ◽  
Dipole Moments ◽  
Equations Of Motion ◽  
Radiation Reaction ◽  
Classical Electrodynamics ◽  
Electric Dipole Moments ◽  
Gauge Invariant ◽  
Intrinsic Angular Momentum

We consider particles with mass, charge, intrinsic magnetic and electric dipole moments, and intrinsic angular momentum in interaction with a classical electromagnetic field. From this action we derive the equations of motion of the position and intrinsic angular momentum of the particle including the radiation reaction, the wave equations of the fields, the current density, and the energy-momentum and angular momentum of the system. The theory is covariant with respect to the general Lorentz group, is gauge invariant, and contains no divergent integrals.

scholarly journals THE PROPER TIME EQUATION AND THE ZAMOLODCHIKOV METRIC

1996 ◽  
Vol 11 (16) ◽  
pp. 2887-2906 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Electromagnetic Field ◽  
Renormalization Group ◽  
Vector Field ◽  
Proper Time ◽  
Beta Function ◽  
Open String ◽  
Point Function ◽  
Gauge Invariant ◽  
Electromagnetic Field Strength ◽  
Uniform Electromagnetic Field

The connection between the proper time equation and the Zamolodchikov metric is discussed. The connection is twofold. First, as already known, the proper time equation is the product of the Zamolodchikov metric and the renormalization group beta function. Second, the condition that the two-point function is the Zamolodchikov metric implies the proper time equation. We study the massless vector of the open string in detail. In the exactly calculable case of a uniform electromagnetic field strength we recover the Born-Infeld equation. We describe the systematics of the perturbative evaluation of the gauge-invariant proper time equation for the massless vector field. The method is valid for nonuniform fields and gives results that are exact to all orders in derivatives. As a nontrivial check, we show that in the limit of uniform fields it reproduces the lowest order Born-Infeld equation.

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