12,147 research outputs found
Vector Casimir effect for a D-dimensional sphere
The Casimir energy or stress due to modes in a D-dimensional volume subject
to TM (mixed) boundary conditions on a bounding spherical surface is
calculated. Both interior and exterior modes are included. Together with
earlier results found for scalar modes (TE modes), this gives the Casimir
effect for fluctuating ``electromagnetic'' (vector) fields inside and outside a
spherical shell. Known results for three dimensions, first found by Boyer, are
reproduced. Qualitatively, the results for TM modes are similar to those for
scalar modes: Poles occur in the stress at positive even dimensions, and cusps
(logarithmic singularities) occur for integer dimensions . Particular
attention is given the interesting case of D=2.Comment: 20 pages, 1 figure, REVTe
Families of particles with different masses in PT-symmetric quantum field theory
An elementary field-theoretic mechanism is proposed that allows one
Lagrangian to describe a family of particles having different masses but
otherwise similar physical properties. The mechanism relies on the observation
that the Dyson-Schwinger equations derived from a Lagrangian can have many
different but equally valid solutions. Nonunique solutions to the
Dyson-Schwinger equations arise when the functional integral for the Green's
functions of the quantum field theory converges in different pairs of Stokes'
wedges in complex field space, and the solutions are physically viable if the
pairs of Stokes' wedges are PT symmetric.Comment: 4 pages, 3 figure
Chaotic systems in complex phase space
This paper examines numerically the complex classical trajectories of the
kicked rotor and the double pendulum. Both of these systems exhibit a
transition to chaos, and this feature is studied in complex phase space.
Additionally, it is shown that the short-time and long-time behaviors of these
two PT-symmetric dynamical models in complex phase space exhibit strong
qualitative similarities.Comment: 22 page, 16 figure
Exact PT-Symmetry Is Equivalent to Hermiticity
We show that a quantum system possessing an exact antilinear symmetry, in
particular PT-symmetry, is equivalent to a quantum system having a Hermitian
Hamiltonian. We construct the unitary operator relating an arbitrary
non-Hermitian Hamiltonian with exact PT-symmetry to a Hermitian Hamiltonian. We
apply our general results to PT-symmetry in finite-dimensions and give the
explicit form of the above-mentioned unitary operator and Hermitian Hamiltonian
in two dimensions. Our findings lead to the conjecture that non-Hermitian
CPT-symmetric field theories are equivalent to certain nonlocal Hermitian field
theories.Comment: Few typos have been corrected and a reference update
On the eigenproblems of PT-symmetric oscillators
We consider the non-Hermitian Hamiltonian H=
-\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a
polynomial of degree at most n \geq 1 with all nonnegative real coefficients
(possibly P\equiv 0). It is proved that the eigenvalues \lambda must be in the
sector | arg \lambda | \leq \frac{\pi}{2n+3}. Also for the case
H=-\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the
eigenfunction u and its derivative u^\prime and we find some other interesting
properties of eigenfunctions.Comment: 21pages, 9 figure
Spontaneous Symmetry Breaking of phi4(1+1) in Light Front Field Theory
We study spontaneous symmetry breaking in phi^4_(1+1) using the light-front
formulation of the field theory. Since the physical vacuum is always the same
as the perturbative vacuum in light-front field theory the fields must develop
a vacuum expectation value through the zero-mode components of the field. We
solve the nonlinear operator equation for the zero-mode in the one-mode
approximation. We find that spontaneous symmetry breaking occurs at
lambda_critical = 4 pi(3+sqrt 3), which is consistent with the value
lambda_critical = 54.27 obtained in the equal time theory. We calculate the
value of the vacuum expectation value as a function of the coupling constant in
the broken phase both numerically and analytically using the delta expansion.
We find two equivalent broken phases. Finally we show that the energy levels of
the system have the expected behavior within the broken phase.Comment: 17 pages, OHSTPY-HEP-TH-92-02
Universality in Random Walk Models with Birth and Death
Models of random walks are considered in which walkers are born at one
location and die at all other locations with uniform death rate. Steady-state
distributions of random walkers exhibit dimensionally dependent critical
behavior as a function of the birth rate. Exact analytical results for a
hyperspherical lattice yield a second-order phase transition with a nontrivial
critical exponent for all positive dimensions . Numerical studies
of hypercubic and fractal lattices indicate that these exact results are
universal. Implications for the adsorption transition of polymers at curved
interfaces are discussed.Comment: 11 pages, revtex, 2 postscript figure
PT-symmetry and its spontaneous breakdown explained by anti-linearity
The impact of an anti-unitary symmetry on the spectrum of non-Hermitian operators is studied. Wigner's normal form of an anti-unitary operator accounts for the spectral properties of non-Hermitian, PE-symmetric Harniltonians. The occurrence of either single real or complex conjugate pairs of eigenvalues follows from this theory. The corresponding energy eigenstates span either one- or two-dimensional irreducible representations of the symmetry PE. In this framework, the concept of a spontaneously broken PE-symmetry is not needed
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