arXiv subjects

H. Toyoda

Publications and source records attributed to H. Toyoda.

4 recordsLinked to original sources

arXiv2014

Noncommutative Spacetime Realized in $AdS_{n+1}$ Space

In $κ$-Minkowski spacetime, the coordinates are Lie algebraic elements such that time and space coordinates do not commute, whereas space coordinates commute each other. The non-commutativity is proportional to a Planck-length-scale constant $κ^{-1}$, which is a universal constant other than the light velocity under the $κ$-Poincare transformation. In this sense, the spacetime has a structure called as "Doubly Special Relativity". Such a noncommutative structure is known to be realized by SO(1,4) generators in 4-dimensional de Sitter space. In this paper, we try to construct a nonommutative spacetime having commutative n-dimensional Minkowski spacetime based on $AdS_{n+1}$ space with SO(2,n) symmetry. We also study an invariant wave equation corresponding to the first Casimir invariant of this symmetry as a non-local field equation expected to yield finite loop amplitudes.

hep-th↗

arXiv2010

A Dynamical System with Q-deformed Phase Space Represented in Ordinary Variable Spaces

Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a difference operator instead of the differential operator. Then, using the path integral representation for such a dynamical system, we derive an effective short-time action, which contains interaction terms even for a free particle with q-deformed phase space. Analysis is also made on the eigenvalue problem for a particle with q-deformed phase space confined in a compact space. Under some boundary conditions of the compact space, there arises fairly different structures from $q=1$ case in the energy spectrum of the particle and in the corresponding eigenspace .

math-ph↗

arXiv2007

An Approach to SU_q(2)p Gauge Theory

In the usual approach to q-deformed gauge theories, the gauge fields are required to be non-local or non-commutative one's. If we introduce, however, an extended product, which we call `` $\star$-product\rq\rq, among the generators of a q-deformed Lie group, the deformed group can be reduced to a ordinary Lie group under the $\star$-product. According to this line of approach, we try to construct a $[SU_q(2)\times U(1)]_\star$, a $SU(2)\times U(1)$ analogue under the $\star$-product, gauge theory. In this gauge theory with the $\star$-product, the U(1) symmetry is naturally incorporated into the SU(2) symmetry. We also study the symmetry breaking by the Higgs mechanism associated with $J=1/2$ and J=1 representations of $SU_q(2)$ algebra, and show that the mixing angle between the SU(2) and U(1) gauge fields is determined uniquely in a tree level.

hep-th↗

arXiv2003

5 Dimensional Spacetime with q-deformed Extra Space

An attempt to get a non-trivial-mass structure of particles in a Randall-Sundrum type of 5-dimensional spacetime with q-deformed extra dimension is discussed. In this spacetime, the fifth dimensional space is boundary free, but there areises an elastic potential preventing free motion toward the fifth direction. The q-deformation is, then, introduced in such a way that the spacetime coordinates become non-commutative between 4-dimensional components and the fifth component. As a result of this q-deformation, there arises naturally an ultraviolet-cutoff effect for the propagators of particles embedded in this spacetime.

hep-th↗