scholarly journals Reparametrization Invariance and Some of the Key Properties of Physical Systems

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 522
Author(s):  
Vesselin G. Gueorguiev ◽  
Andre Maeder
Keyword(s):  
Proper Time ◽  
Hamiltonian Formulation ◽  
Hamiltonian Constraint ◽  
Negative Mass ◽  
Principle Of Superposition ◽  
Physical Systems ◽  
First Order ◽  
Classical Phase Space ◽  
Generally Covariant ◽  
Reparametrization Invariance

In this paper, we argue in favor of first-order homogeneous Lagrangians in the velocities. The relevant form of such Lagrangians is discussed and justified physically and geometrically. Such Lagrangian systems possess Reparametrization Invariance (RI) and explain the observed common Arrow of Time as related to the non-negative mass for physical particles. The extended Hamiltonian formulation, which is generally covariant and applicable to reparametrization-invariant systems, is emphasized. The connection between the explicit form of the extended Hamiltonian H and the meaning of the process parameter λ is illustrated. The corresponding extended Hamiltonian H defines the classical phase space-time of the system via the Hamiltonian constraint H=0 and guarantees that the Classical Hamiltonian H corresponds to p0—the energy of the particle when the coordinate time parametrization is chosen. The Schrödinger’s equation and the principle of superposition of quantum states emerge naturally. A connection is demonstrated between the positivity of the energy E=cp0>0 and the normalizability of the wave function by using the extended Hamiltonian that is relevant for the proper-time parametrization.

Mixed State Hamiltonian Element for Plane Transversely Isotropic Magnetoelectroelastic Solids

2013 ◽  
Vol 275-277 ◽  
pp. 1978-1983
Author(s):  
Xiao Chuan Li ◽  
Jin Shuang Zhang
Keyword(s):  
Mixed State ◽  
Hamiltonian Formulation ◽  
Transversely Isotropic ◽  
Laminated Plates ◽  
Governing Equations ◽  
Time Coordinate ◽  
First Order ◽  
Linear Elements ◽  
Propagation Matrix ◽  
Magnetoelectroelastic Solids

Hamiltonian dual equation of plane transversely isotropic magnetoelectroelastic solids is derived from variational principle and mixed state Hamiltonian elementary equations are established. Similar to the Hamiltonian formulation in classic dynamics, the z coordinate is treated analogous to the time coordinate. Then the x-direction is discreted with the linear elements to obtain the state-vector governing equations, which are a set of first order differential equations in z and are solved by the analytical approach. Because present approach is analytic in z direction, there is no restriction on the thickness of plate through the use of the present element. Using the propagation matrix method, the approach can be extended to analyze the problems of magnetoelectroelastic laminated plates. Present semi-analytical method of mixed Hamiltonian element has wide application area.

scholarly journals Method of Third-Order Convergence with Approximation of Inverse Operator for Large Scale Systems

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 978
Author(s):  
Ioannis K. Argyros ◽  
Stepan Shakhno ◽  
Halyna Yarmola
Keyword(s):  
Large Scale ◽  
Inverse Operator ◽  
Vital Role ◽  
Systems Of Equations ◽  
Third Order ◽  
Large Scale Systems ◽  
Physical Systems ◽  
First Order ◽  
Finite Dimensional ◽  
Abstract Spaces

A vital role in the dynamics of physical systems is played by symmetries. In fact, these studies require the solution for systems of equations on abstract spaces including on the finite-dimensional Euclidean, Hilbert, or Banach spaces. Methods of iterative nature are commonly used to determinate the solution. In this article, such methods of higher convergence order are studied. In particular, we develop a two-step iterative method to solve large scale systems that does not require finding an inverse operator. Instead of the operator’s inverting, it uses a two-step Schultz approximation. The convergence is investigated using Lipschitz condition on the first-order derivatives. The cubic order of convergence is established and the results of the numerical experiment are given to determine the real benefits of the proposed method.

scholarly journals NAMBU-JONA-LASINIO MODEL IN CURVED SPACE-TIME

1993 ◽  
Vol 08 (22) ◽  
pp. 2117-2123 ◽  
Author(s):  
T. INAGAKI ◽  
T. MUTA ◽  
S.D. ODINTSOV
Keyword(s):  
Proper Time ◽  
Space Time ◽  
Leading Order ◽  
Coupling Constant ◽  
Normal Coordinate ◽  
Dynamical Mass ◽  
Curved Space ◽  
First Order ◽  
First Order Phase Transition ◽  
First Order Phase

The phase structure of Nambu-Jona-Lasinio model with N-component fermions in curved space-time is studied in the leading order of the 1/N expansion. The effective potential for composite operator [Formula: see text] is calculated by using the normal coordinate expansion in the Schwinger proper-time method. The existence of the first order phase transition caused by the change of the space-time curvature is confirmed and the dynamical mass of the fermion is calculated as a simultaneous function of the curvature and the four-fermion coupling constant. The phase diagram in the curvature and the coupling constant is obtained.

scholarly journals Swanson hamiltonian: non-PT-symmetry phase

2021 ◽  
Author(s):  
Viviano Fernández ◽  
Romina Ramirez ◽  
Marta Reboiro
Keyword(s):  
Infinite Order ◽  
Model Space ◽  
Pt Symmetry ◽  
Negative Mass ◽  
Physical Systems ◽  
Exceptional Points ◽  
Symmetry Phase ◽  
Generalized Eigenfunctions

Abstract In this work, we study the non-hermitian Swanson hamiltonian, particularly the non-PT symmetry phase. We use the formalism of Gel’fand triplet to construct the generalized eigenfunctions and the corresponding spectrum. Depending on the region of the parameter model space, we show that the Swanson hamiltonian represents different physical systems, i.e. parabolic barrier, negative mass oscillators. We also discussed the presence of Exceptional Points of infinite order.

scholarly journals REMARKS ON PURE SPIN CONNECTION FORMULATIONS OF GRAVITY

1992 ◽  
Vol 07 (21) ◽  
pp. 1871-1877 ◽  
Author(s):  
RICCARDO CAPOVILLA ◽  
TED JACOBSON
Keyword(s):  
Hamiltonian Formulation ◽  
Lagrangian Formulation ◽  
Pure Spin ◽  
Spin Connection ◽  
Action Functional ◽  
First Order

In the derivation of a pure spin connection action functional for gravity, two methods have been proposed. The first starts from a first order Lagrangian formulation, the second from a Hamiltonian formulation. In this note we show that they lead to identical results.

scholarly journals FIRST-ORDER QUANTUM-GRAVITATIONAL CORRECTION TO FRIEDMANNIAN COSMOLOGY FROM COVARIANT, HOLOMORPHIC SPINFOAM COSMOLOGY

2013 ◽  
Vol 22 (02) ◽  
pp. 1350005
Author(s):  
CHRISTIAN RÖKEN
Keyword(s):  
Cosmological Model ◽  
Loop Quantum Gravity ◽  
Transition Amplitude ◽  
Hamiltonian Constraint ◽  
Planck Constant ◽  
First Order ◽  
Quantum Hamiltonian ◽  
Expansion Of The Universe ◽  
General Relativistic ◽  
The Universe

The first-order loop quantum gravity correction of the simplest, classical general relativistic Friedmann Hamiltonian constraint, emerging from a holomorphic spinfoam cosmological model peaked on homogeneous, isotropic geometries, is studied. A quantum Hamiltonian constraint satisfied by the EPRL transition amplitude between the boundary cosmological coherent states includes a contribution of the order of the Planck constant ℏ that also appears in the corresponding semiclassical, symplectic model. The analysis of this term gives a quantum-gravitational correction to the classical Friedmann dynamics of the scale factor yielding an insignificantly small deceleration contribution in the expansion of the universe. The robustness of the physical interpretation is established for arbitrary refinements of the boundary graphs. Also, mathematical equivalences between the semiclassical cosmological model and certain classical fluid and scalar field theories are explored.

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