scholarly journals On the Synergic Relationships between Special Relativity and Quantum Theories

2020 ◽  
pp. 34-43
Author(s):  
E. Comay
Keyword(s):  
Lagrangian Density ◽  
Energy Momentum Tensor ◽  
Quantum Particle ◽  
Momentum Tensor ◽  
Lagrange Equations ◽  
Quantum Theories ◽  
Hamiltonian Density ◽  
Relativistic Form ◽  
Lorentz Scalar ◽  
Conservation Laws Of Energy

The successful results of the relativistic form of a quantum field theory that is derived from aLagrangian density justify its general usage. The significance of the Euler-Lagrange equations of a quantum particle is analysed. Many advantages of this approach, like abiding by the conservation laws of energy, momentum, angular momentum, and charge are well known. The merits of this approach also include other properties that are still not well known. For example, it is shown that a quantum function of the form ψ(t, r) describes a pointlike particle. Furthermore, the Lagrangian density and the Hamiltonian density take a different relativistic form – the Lagrangian density is a Lorentz scalar, whereas the Hamiltonian density is the T00 component of the energy-momentum tensor. It is proved that inconsistencies in the electroweak theory stem from negligence of the latter point.

scholarly journals Relativistic Properties of a Lagrangian and a Hamiltonian in Quantum Theories

2019 ◽  
pp. 1-9
Author(s):  
Eliahu Comay
Keyword(s):  
Lagrangian Density ◽  
Energy Momentum Tensor ◽  
Weak Interactions ◽  
Axial Vector ◽  
Momentum Tensor ◽  
Tensor Interaction ◽  
Quantum Theories ◽  
Hamiltonian Density ◽  
Lorentz Scalar ◽  
Interaction Term

Relativistic properties of a Dirac Lagrangian density are compared with those of a Dirac Hamiltonian density. Differences stem from the fact that a Lagrangian density is a Lorentz scalar, whereas a Hamiltonian density is a 00-component of a second rank tensor, called the energy-momentum tensor. This distinction affects the form of an interaction term of a Dirac particle. In particular, a tensor interaction term of a Dirac Lagrangian density transforms to a difference between a vector and an axial vector of the corresponding Hamiltonian density. This outcome shows that fundamental principles can prove the V-A attribute of weak interactions. A further analysis supports these results. Inherent problems of the electroweak theory are discussed.

scholarly journals On the Significance of the Fields’ Energy-Momentum Tensor

2019 ◽  
pp. 1-9
Author(s):  
E. Comay
Keyword(s):  
Quantum Electrodynamics ◽  
Lagrangian Density ◽  
Order Differential Equation ◽  
Energy Momentum Tensor ◽  
Massive Particle ◽  
Momentum Tensor ◽  
Noether Theorem ◽  
Consistency Test ◽  
Independent Analysis ◽  
Physical Fields

This work discusses the significance of the energy-momentum tensor of physical fields of an elementary particle. The Noether theorem shows how this tensor can be derived from the Lagrangian density of a given field. This work proves that the energy-momentum tensor can also be used for a consistency test of a field theory. The results show that the Dirac Lagrangian density of a spin-1/2 massive particle yields consistent results. On the other hand, problems exist with the present structure of quantum electrodynamics, and with quantum fields of massive particles that are described by a second order differential equation. All problematic results are confirmed by an independent analysis.

scholarly journals A Spin-Perturbation for Minimal Surfaces

2021 ◽  
Author(s):  
Ruijun Wu
Keyword(s):  
Minimal Surface ◽  
Minimal Surfaces ◽  
Energy Momentum Tensor ◽  
Harmonic Maps ◽  
Momentum Tensor ◽  
Lagrange Equations ◽  
Surface Equation ◽  
Minimal Surface Equation ◽  
Volume Functional

AbstractWe investigate the coupling of the minimal surface equation with a spinor of harmonic type. This arises as the Euler–Lagrange equations of the sum of the volume functional and the Dirac action, defined on an appropriated Dirac bundle. The solutions show a relation to Dirac-harmonic maps under some constraints on the energy-momentum tensor, extending the relation between Riemannian minimal surface and harmonic maps.

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.

scholarly journals Second-order integrable Lagrangians and WDVV equations

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
E. V. Ferapontov ◽  
M. V. Pavlov ◽  
Lingling Xue
Keyword(s):  
Lagrangian Density ◽  
Theta Functions ◽  
Second Order ◽  
Elementary Functions ◽  
Lagrange Equations ◽  
Wdvv Equations ◽  
Integrability Conditions ◽  
Jacobi Theta Functions

AbstractWe investigate the integrability of Euler–Lagrange equations associated with 2D second-order Lagrangians of the form $$\begin{aligned} \int f(u_{xx},u_{xy},u_{yy})\ \mathrm{d}x\mathrm{d}y. \end{aligned}$$ ∫ f ( u xx , u xy , u yy ) d x d y . By deriving integrability conditions for the Lagrangian density f, examples of integrable Lagrangians expressible via elementary functions, Jacobi theta functions and dilogarithms are constructed. A link of second-order integrable Lagrangians to WDVV equations is established. Generalisations to 3D second-order integrable Lagrangians are also discussed.

scholarly journals Cutoff AdS3 versus $$ T\overline{T} $$ CFT2 in the large central charge sector: correlators of energy-momentum tensor

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yi Li ◽  
Yang Zhou
Keyword(s):  
Field Theory ◽  
Euclidean Plane ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Momentum Tensor ◽  
Two Dimensional ◽  
Conformal Field ◽  
Operator Identity ◽  
Pure Gravity ◽  
Charge Sector

Abstract In this article we probe the proposed holographic duality between $$ T\overline{T} $$ T T ¯ deformed two dimensional conformal field theory and the gravity theory of AdS3 with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $$ T\overline{T} $$ T T ¯ CFT in a Euclidean plane and a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in Euclidean AdS3 with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $$ T\overline{T} $$ T T ¯ CFT parameters.

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