A note on the relativistic invariance of quantized field theories

1950 ◽  
Vol 46 (2) ◽  
pp. 316-318
Author(s):  
J. S. de Wet
Keyword(s):  
Present Author ◽  
Higher Order ◽  
Field Theories ◽  
Poisson Brackets ◽  
Relativistic Invariance ◽  
Field Equations ◽  
Commutation Relations ◽  
Generalized Poisson ◽  
Quantized Field

In an earlier paper (1), which will be referred to as A, the present author has demonstrated the relativistic invariance, for general transformations of coordinates, of the Einstein-Bose and Fermi-Dirac quantizations of linear field equations derived from higher order Lagrangians. The proof consisted of the identification of the commutation relations with the generalized Poisson brackets introduced by Weiss (2) and proving the invariance of the latter.

scholarly journals On the relativistic invariance of quantized field theories

1948 ◽  
Vol 195 (1042) ◽  
pp. 365-376 ◽  
Keyword(s):  
Present Author ◽  
Higher Order ◽  
Field Theories ◽  
Relativistic Invariance ◽  
Field Equations ◽  
First Order ◽  
Generalized Poisson ◽  
General Relativistic ◽  
Quantized Field ◽  
Derivatives Of

Heisenberg & Pauli (1929) have shown how to quantize field theories derived from Lagrangians containing first-order derivatives of the field quantities. They showed their quantization to be Lorentz invariant. Fuchs (1939) subsequently showed that the quantized theory was in fact invariant under general transformations of co-ordinates. The present author in another paper has shown how the theory of Heisenberg & Pauli can be extended to field equations derived from higher order Lagrangians, i. e. Lagrangians containing higher deri­vatives than the first of the field quantities. In the present paper the general relativistic invariance of the higher order quantized theories is established, making use of the generalized Poisson brackets introduced by Weiss.

scholarly journals Quantum electrodynamics with ∂ A μ /∂ x μ = 0

1946 ◽  
Vol 185 (1001) ◽  
pp. 192-206 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Quantum Electrodynamics ◽  
Maxwell Equations ◽  
Poisson Brackets ◽  
Relativistic Invariance ◽  
Field Equations ◽  
Vacuum Case ◽  
Commutation Relations ◽  
Longitudinal Part

The quantization of the electromagnetic field subject to ∂ A μ /∂ x μ = 0 ( A μ being the four-potential) developed in an earlier paper is reviewed, and a proof of the relativistic invariance of the commutation relations left out in the earlier paper supplied (§ 2). The Poisson brackets of A μ at two different points in space are worked out for the vacuum case (§ 3). If, instead of considering a field of matter, one considers explicitly different particles interacting with the electromagnetic field, such a theory gives us field equations which differ slightly from the equations of Dirac, Fock & Podolsky. By imposing a condition on Ψ occurring in nature, the Maxwell equations remain satisfied (§ 4, 5). Finally, it is shown how the equation ∂ A μ /∂ x μ = 0 can be brought into the new electrodynamics of Dirac and how, as a consequence, the longitudinal part of the field can be eliminated (§ 6).

On the quantization of field theories derived from higher order lagrangians

1948 ◽  
Vol 44 (4) ◽  
pp. 546-559 ◽  
Author(s):  
J. S. de Wet
Keyword(s):  
Energy Momentum Tensor ◽  
Present Theory ◽  
Momentum Tensor ◽  
Higher Order ◽  
Field Theories ◽  
Hamiltonian Form ◽  
Field Equations ◽  
Dirac Quantization ◽  
Higher Derivatives ◽  
Derivatives Of

Heisenberg and Pauli (1) have shown how to quantize field theories derived from a Lagrangian containing first derivatives of the field quantities only. The present paper extends the theory of quantization of fields to the case of higher order Lagrangians, i.e. Lagrangians in which higher derivatives than the first appear. It is shown how such field equations can be put into Hamiltonian form and how the quantization can subsequently be carried out. Both the cases of Einstein-Bose and Fermi-Dirac quantization are discussed. It is established that the quantization is relativistically invariant and consistent with the field equations. An interesting feature of the present theory is that the Hamiltonian proves to be different, in general, from the integral of the 4–4 component of the energy momentum tensor.

scholarly journals THE SOLUTIONS OF AFFINE AND CONFORMAL AFFINE TODA FIELD THEORIES

1994 ◽  
Vol 09 (17) ◽  
pp. 1579-1587 ◽  
Author(s):  
G. PAPADOPOULOS ◽  
B. SPENCE
Keyword(s):  
Initial Data ◽  
Minkowski Space ◽  
Space Time ◽  
Field Theories ◽  
Poisson Brackets ◽  
Two Dimensional ◽  
Field Equations ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space ◽  
Static Solutions

We give new formulations of the solutions of the field equations of the affine Toda and conformal affine Toda theories on a cylinder and two-dimensional Minkowski space-time. These solutions are parametrized in terms of initial data and the resulting covariant phase spaces are diffeomorphic to the Hamiltonian ones. We derive the fundamental Poisson brackets to the parameters of the solutions and give the general static solutions for the affine theory.

scholarly journals HIGHER-ORDER CURVATURE TERMS IN BORN–INFELD TYPE BRANE THEORIES

2011 ◽  
Vol 20 (01) ◽  
pp. 59-75 ◽  
Author(s):  
EFRAIN ROJAS
Keyword(s):  
Ricci Tensor ◽  
General Structure ◽  
Extrinsic Curvature ◽  
Higher Order ◽  
Square Root ◽  
Auxiliary Variables ◽  
Field Equations ◽  
Alternative Description ◽  
Brane Models ◽  
Combined Matrix

The field equations associated to Born–Infeld type brane theories are studied by using auxiliary variables. This approach hinges on the fact, that the expressions defining the physical and geometrical quantities describing the worldvolume are varied independently. The general structure of the Born–Infeld type theories for branes contains the square root of a determinant of a combined matrix between the induced metric on the worldvolume swept out by the brane and a symmetric/antisymmetric tensor depending on gauge, matter or extrinsic curvature terms taking place on the worldvolume. The higher-order curvature terms appearing in the determinant form come to play in competition with other effective brane models. Additionally, we suggest a Born–Infeld–Einstein type action for branes where the higher-order curvature content is provided by the worldvolume Ricci tensor. This action provides an alternative description of the dynamics of braneworld scenarios.

scholarly journals May the four be with you: novel IR-subtraction methods to tackle NNLO calculations

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
W. J. Torres Bobadilla ◽  
G. F. R. Sborlini ◽  
P. Banerjee ◽  
S. Catani ◽  
A. L. Cherchiglia ◽  
...  
Keyword(s):  
High Energy Physics ◽  
High Energy ◽  
Higher Order ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Link Type ◽  
Mathematical Properties ◽  
Energy Physics ◽  
The Way

AbstractIn this manuscript, we report the outcome of the topical workshop: paving the way to alternative NNLO strategies (https://indico.ific.uv.es/e/WorkStop-ThinkStart_3.0), by presenting a discussion about different frameworks to perform precise higher-order computations for high-energy physics. These approaches implement novel strategies to deal with infrared and ultraviolet singularities in quantum field theories. A special emphasis is devoted to the local cancellation of these singularities, which can enhance the efficiency of computations and lead to discover novel mathematical properties in quantum field theories.

scholarly journals Generalizing the coupling between geometry and matter: $$f\left( R,L_m,T\right) $$ gravity

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Zahra Haghani ◽  
Tiberiu Harko
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Newtonian Limit ◽  
Gravity Models ◽  
Momentum Balance ◽  
Field Equations ◽  
Gravitational Fields ◽  
Generalized Poisson

AbstractWe generalize and unify the $$f\left( R,T\right) $$ f R , T and $$f\left( R,L_m\right) $$ f R , L m type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R, of the trace of the energy–momentum tensor T, and of the matter Lagrangian $$L_m$$ L m , so that $$ L_{grav}=f\left( R,L_m,T\right) $$ L grav = f R , L m , T . We obtain the gravitational field equations in the metric formalism, the equations of motion for test particles, and the energy and momentum balance equations, which follow from the covariant divergence of the energy–momentum tensor. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equations of motion is also investigated, and the expression of the extra acceleration is obtained for small velocities and weak gravitational fields. The generalized Poisson equation is also obtained in the Newtonian limit, and the Dolgov–Kawasaki instability is also investigated. The cosmological implications of the theory are investigated for a homogeneous, isotropic and flat Universe for two particular choices of the Lagrangian density $$f\left( R,L_m,T\right) $$ f R , L m , T of the gravitational field, with a multiplicative and additive algebraic structure in the matter couplings, respectively, and for two choices of the matter Lagrangian, by using both analytical and numerical methods.

Derivative expansions for affinely quantized field theories. II. Scale-invariant quantization

1992 ◽  
Vol 45 (12) ◽  
pp. 4600-4609
Author(s):  
R. J. Rivers ◽  
C. C. Wong ◽  
Carl M. Bender
Keyword(s):  
Field Theories ◽  
Scale Invariant ◽  
Quantized Field

Higher-Order Theories for Structural Analysis Using Legendre Polynomial Expansions

1969 ◽  
Vol 36 (4) ◽  
pp. 757-762 ◽  
Author(s):  
A. I. Soler
Keyword(s):  
Structural Analysis ◽  
Legendre Polynomials ◽  
Direct Reduction ◽  
Beam Theory ◽  
Plane Elasticity ◽  
Higher Order ◽  
Governing Equations ◽  
Field Equations ◽  
Displacement Boundary ◽  
Polynomial Expansions

Governing equations of plane elasticity are examined to define suitable approximate theories. Each dependent variable in the problem is considered as a series expansion in Legendre polynomials; attention is focused on establishment of a logical approach to truncation of the series. Important variables for approximate theories of any order are established from energy considerations, and the desired approximate theories are established by direct reduction of the field equations and also from an energy viewpoint. A new “classical” beam theory is developed capable of treating displacement boundary conditions on lateral surfaces. Higher-order approximate theories are studied to make certain comparisons with exact solutions; the results of these comparisons indicate that the new method yields approximate theories which may be more accurate than previous theories with similar levels of approximation.

A Note on Commutators in Quantized Field Theories

1950 ◽  
Vol 78 (5) ◽  
pp. 613-614 ◽  
Author(s):  
S. Schweber
Keyword(s):  
Field Theories ◽  
Quantized Field
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