Theory of the relativistic spinning particle: Hamiltonian formulation and world-line invariance

1984 ◽  
Vol 30 (8) ◽  
pp. 1707-1711 ◽  
Author(s):  
Kenneth Rafanelli
Keyword(s):  
World Line ◽  
Hamiltonian Formulation ◽  
Spinning Particle

scholarly journals Yukawa couplings for the spinning particle and the world-line formalism

1995 ◽  
Vol 351 (1-3) ◽  
pp. 200-205 ◽  
Author(s):  
Myriam Mondragón ◽  
Lukas Nellen ◽  
Michael G. Schmidt ◽  
Christian Schubert
Keyword(s):  
World Line ◽  
Spinning Particle ◽  
Yukawa Couplings ◽  
The World

World-line condition for a spinning particle in superspace

1984 ◽  
Vol 82 (1) ◽  
pp. 17-28 ◽  
Author(s):  
J. Gomis ◽  
P. Mato ◽  
M. Novell
Keyword(s):  
World Line ◽  
Spinning Particle ◽  
Line Condition

World-line geometry probed by fast spinning particle

2015 ◽  
Vol 30 (21) ◽  
pp. 1550101 ◽  
Author(s):  
Alexei A. Deriglazov ◽  
Walberto Guzmán Ramírez
Keyword(s):  
General Relativity ◽  
Electromagnetic Field ◽  
Critical Speed ◽  
World Line ◽  
Empty Space ◽  
Line Geometry ◽  
Speed Of Light ◽  
Spinning Particle ◽  
Effective Metric ◽  
The World

Interaction of spin with electromagnetic field yields an effective metric along the world-line of spinning particle with anomalous magnetic moment. If we insist to preserve the usual special relativity definitions of time and distance, critical speed which the particle cannot overcome during its evolution in electromagnetic field differs from the speed of light. Instead, we can follow the general relativity prescription to define time and distance. With these definitions, critical speed coincides with the speed of light. But intervals of time and distance probed by the particle in the presence of electromagnetic field slightly differ from those in empty space. Effective metric arises also when spin interacts with gravitational field.

Shape Dynamics and the Linking Theory

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Line Element ◽  
Hamiltonian Formulation ◽  
Operational Definition ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Problem Of Time ◽  
Definition Of ◽  
Matter Fields

This chapter explains in detail the current Hamiltonian formulation of SD, and the concept of Linking Theory of which (GR) and SD are two complementary gauge-fixings. The physical degrees of freedom of SD are identified, the simple way in which it solves the problem of time and the problem of observables in quantum gravity are explained, and the solution to the problem of constructing a spacetime slab from a solution of SD (and the related definition of physical rods and clocks) is described. Furthermore, the canonical way of coupling matter to SD is introduced, together with the operational definition of four-dimensional line element as an effective background for matter fields. The chapter concludes with two ‘structural’ results obtained in the attempt of finding a construction principle for SD: the concept of ‘symmetry doubling’, related to the BRST formulation of the theory, and the idea of ‘conformogeometrodynamics regained’, that is, to derive the theory as the unique one in the extended phase space of GR that realizes the symmetry doubling idea.

The kinematics of a point particle

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Internal Structure ◽  
Proper Time ◽  
World Line ◽  
Point Particle ◽  
Material Point ◽  
Spatial Extent ◽  
Geometric Representation ◽  
Mathematical Result ◽  
Point Particles ◽  
The World

This chapter discusses the kinematics of point particles undergoing any type of motion. It introduces the concept of proper time—the geometric representation of the time measured by an accelerated clock. It also describes a world line, which represents the motion of a material point or point particle P, that is, an object whose spatial extent and internal structure can be ignored. The chapter then considers the interpretation of the curvilinear abscissa, which by definition measures the length of the world line L representing the motion of the point particle P. Next, the chapter discusses a mathematical result popularized by Paul Langevin in the 1920s, the so-called ‘Langevin twins’ which revealed a paradoxical result. Finally, the transformation of velocities and accelerations is discussed.

General Relativity

2019 ◽  
Author(s):  
Steven Carlip
Keyword(s):  
General Relativity ◽  
High Energy Physics ◽  
Hamiltonian Formulation ◽  
Experimental Tests ◽  
High Energy ◽  
Gravitational Energy ◽  
Field Equations ◽  
Physics First ◽  
Condensed Matter Theory ◽  
Introductory Textbooks

This work is a short textbook on general relativity and gravitation, aimed at readers with a broad range of interests in physics, from cosmology to gravitational radiation to high energy physics to condensed matter theory. It is an introductory text, but it has also been written as a jumping-off point for readers who plan to study more specialized topics. As a textbook, it is designed to be usable in a one-quarter course (about 25 hours of instruction), and should be suitable for both graduate students and advanced undergraduates. The pedagogical approach is “physics first”: readers move very quickly to the calculation of observational predictions, and only return to the mathematical foundations after the physics is established. The book is mathematically correct—even nonspecialists need to know some differential geometry to be able to read papers—but informal. In addition to the “standard” topics covered by most introductory textbooks, it contains short introductions to more advanced topics: for instance, why field equations are second order, how to treat gravitational energy, what is required for a Hamiltonian formulation of general relativity. A concluding chapter discusses directions for further study, from mathematical relativity to experimental tests to quantum gravity.

scholarly journals Currents, charges and algebras in exceptional generalised geometry

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
David Osten
Keyword(s):  
Current Algebra ◽  
Hamiltonian Formulation ◽  
Building Blocks ◽  
Lie Derivative ◽  
Consistency Check ◽  
World Volume ◽  
Invariant Currents ◽  
Invariant Current ◽  
M Theory ◽  
A Current

Abstract A classical Ed(d)-invariant Hamiltonian formulation of world-volume theories of half-BPS p-branes in type IIb and eleven-dimensional supergravity is proposed, extending known results to d ≤ 6. It consists of a Hamiltonian, characterised by a generalised metric, and a current algebra constructed s.t. it reproduces the Ed(d) generalised Lie derivative. Ed(d)-covariance necessitates the introduction of so-called charges, specifying the type of p-brane and the choice of section. For p > 2, currents of p-branes are generically non- geometric due to the imposition of U-duality, e.g. the M5-currents contain coordinates associated to the M2-momentum.A derivation of the Ed(d)-invariant current algebra from a canonical Poisson structure is in general not possible. At most, one can derive a current algebra associated to para-Hermitian exceptional geometry.The membrane in the SL(5)-theory is studied in detail. It is shown that in a generalised frame the current algebra is twisted by the generalised fluxes. As a consistency check, the double dimensional reduction from membranes in M-theory to strings in type IIa string theory is performed. Many features generalise to p-branes in SL(p + 3) generalised geometries that form building blocks for the Ed(d)-invariant currents.

scholarly journals Port-Hamiltonian formulation of two-phase flow models

2021 ◽  
Vol 149 ◽  
pp. 104881
Author(s):  
H. Bansal ◽  
P. Schulze ◽  
M.H. Abbasi ◽  
H. Zwart ◽  
L. Iapichino ◽  
...  
Keyword(s):  
Two Phase Flow ◽  
Hamiltonian Formulation ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Models
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