arXiv subjects

Takayoshi Ootsuka

Publications and source records attributed to Takayoshi Ootsuka.

13 recordsLinked to original sources

arXiv2022

Generalized Mathisson-Papapetrou-Tulczyjew-Dixon Equations

We derive two generalizations of Mathisson-Papapetrou-Tulczyjew-Dixon equations from Casalbuoni-Brink-Schwarz type pseudoclassical Lagrangians of Majorana spinors on a Riemann-Cartan spacetime. One has a "color" freedom, which makes the equations of motion also be a generalization of Wong equations. The other is a spinor model coupled with a Rarita-Schwinger field to preserve the supersymmetry. The coupling to the torsion is modified due to the existence of the Rarita-Schwinger field. In both extensions, the Tulczyjew condition is automatically satisfied.

gr-qc↗

arXiv2018

Finsler connection in moving frame formalism

In our previous work, we have defined a nonlinear connection of Finsler manifold which preserves the Finsler metric $L=L(x,dx)$. To make the method easier and more useful in applications, moving frame (vielbein) $θ^a={e^a}_μdx^μ$ formalism for the nonlinear connection is newly considered. We derive formulae to calculate the Finsler connection in the specific case that the Finsler metric depends not on coordinates $x^μ$, but only on moving frame $θ^a$: $L=L(θ)$.

math-ph↗

arXiv2018

Super Finsler Connection of Superparticle on Two Dimensional Curved Spacetime

We analyze the Casalbuoni-Brink-Schwarz superparticle model on a 2-dimensional curved spacetime as a super Finsler metric defined on a (2,2)-dimensional supermanifold. We propose a nonlinear Finsler connection which preserves this Finsler metric and calculates it explicitly. The equations of motion of the superparticle are reconstructed in the form of auto-parallel equations expressed by the super nonlinear connection.

hep-th↗

arXiv2017

Cusp singularity in mean field Ising model

An entropy of the Ising model in the mean field approximation is derived by the Hamilton-Jacobi formalism. We consider a grand canonical ensemble with respect to the temperature and the external magnetic field. A cusp arises at the critical point, which shows a simple and new geometrical aspect of this model. In educational sense, this curve with a cusp helps students acquire a more intuitive view on statistical phase transitions.

math-ph↗

arXiv2016

Killing Symmetry on Finsler Manifold

Killing vector fields $K$ are defined on Finsler manifold. The Killing symmetry is reformulated simply as $δK^\flat =0$ by using the Killing non-linear 1-form $K^\flat$ and the spray operator $δ$ with the Finsler non-linear connection. $K^\flat$ is related to the generalization of Killing tensors on Finsler manifold, and the condition $δK^\flat =0$ gives an analytical method of finding higher derivative conserved quantities, which may be called hidden conserved quantities. We show two examples: the Carter constant on Kerr spacetime and the Runge-Lentz vectors in Newtonian gravity.

gr-qc↗

arXiv2016

Variational principle of relativistic perfect fluid

We reformulate the relativistic perfect fluid system on curved space-time. Using standard variables, the velocity field $u$,energy density $ρ$ and pressure $p$, the covariant Euler-Lagrange equation is obtained from variational principle. This leads to the Euler equation and the equation of continuity in reparametrization invariant form.

gr-qc↗

arXiv2016

Finsler connection for general Lagrangian systems

We give a Finsler non-linear connection by a new simplified definition for not only regular case but also singular case. In regular case, it corresponds to non-linear connection part of Berwald's connection, but our connection is expressed not in line element space but in point-Finsler space. In this view we recognize Finsler metric L(x,dx) as a non-linear form, which is a natural generalisation of Riemannian metric having original expression, \sqrt{g_{ab}(x)dx^a dx^b}. Furthermore our formulae provide easier calculation rather than conventional treatments, so we think that they suits to application to physics. Our definition can be used in the singular case of Finsler metric, which correspond to gauged constraint systems in mechanics. Here we give some non trivial examples of constraint systems for exposition of validity of our connection.

math.DG↗

arXiv2015

Energy-momentum conservation laws in Finsler/Kawaguchi Lagrangian formulation

We reformulate the standard Lagrangian formalism to a reparameterisation invariant Lagrangian formalism by means of Finsler and Kawaguchi geometry. In our formalism, various types of symmetries that appears in theories of physics are expressed geometrically by symmetries of Finsler (Kawaguchi) metric, and the conservation law of energy-momentum is a part of Euler-Lagrange equations. The application to scalar field, Dirac field, electromagnetic field and general relativity coupled to perfect fluid (added: ver.3) are discussed. By this formalism, we try to propose an alternative definition of energy-momentum current of gravity.

gr-qc↗

arXiv2010

Finsler Geometrical Path Integral

A new definition for the path integral is proposed in terms of Finsler geometry. The conventional Feynman's scheme for quantisation by Lagrangian formalism suffers problems due to the lack of geometrical structure of the configuration space where the path integral is defined. We propose that, by implementing the Feynman's path integral on an extended configuration space endowed with a Finsler structure, the formalism could be justified as a proper scheme for quantisation from Lagrangian only, that is, independent from Hamiltonian formalism. The scheme is coordinate free, and also a covariant framework which does not depend on the choice of time coordinate.

hep-th↗

arXiv2005

Non-associative Gauge Theory

We present a construction of gauge theory which its structure group is not a Lie group, but a Moufang loop which is essentially non-associative. As an example of non-associative algebra, we take octonions with norm one as a Moufang loop, with which we can produce an octonionic gauge theory. Our octonionic gauge theory is a natural generalization of Maxwell U(1)= S^1 gauge theory and Yang-Mills SU(2)= S^3 gauge theory. We also give the BPST like instanton solution of our octonionic gauge theory in 8 dimension.

hep-th↗

arXiv2003

Chiral gravity in higher dimensions

We construct a chiral theory of gravity in 7 and 8 dimensions, which are equivalent to Einstein-Cartan theory using less variables. In these dimensions, we can construct such higher dimensional chiral gravity because of the existence of gravitational instanton. The octonionic-valued variables in the theory represent the deviation from the gravitational instanton, and from their non-associativity, prevents the theory to be SO(n) gauge invariant. Still the chiral gravity holds G_2 (7-D), and Spin(7) (8-D) gauge symmetry.

gr-qc↗

arXiv2000

Macroscopic quantum tunneling of the Bose-Einstein condensate trapped in cylindrically symmetric potential

We investigate the macroscopic quantum tunneling of the attractive Bose-Einstein condensate. Within the effective Lagrangian framework, we find bounce solutions and explicitly calculate the decay rate of the condensate trapped in a cylindrically symmetric potential. In particular, in the case where the number of condensed bosons is slightly below a certain critical number, we present a detailed analysis of the bounce solutions and discuss the approximations employed in our calculations. The effects of finite temperatures and the shape of the trapping potential are evaluated.

cond-mat↗

arXiv2000

Spin(7) holonomy manifold and Superconnection

We discuss the higher dimensional generalization of gravitational instantons by using volume-preserving vector fields. We give special attention to the case of 8-dimensions and present a new construction of the Ricci flat metric with holonomy in Spin(7). An example of the metric is explicitly given. Further it is shown that our formulation has a natural interpretation in the Chern-Simons theory written by the language of superconnections.

hep-th↗