64 research outputs found
Zero and finite temperature Casimir effect of massive vector field between real metals
We consider the Casimir effect of a massive vector field between two
semi-infinite dielectric slabs. We first derive the generalization of the
Lifshitz formula that gives the Casimir interaction energy of two
magnetodielectric slabs separated by a magnetodielectric medium due to the
vacuum fluctuations of a massive vector field. We then discuss the asymptotic
behaviors of the Casimir energy and the Casimir force in various limits, such
as low temperature, high temperature, small mass, large mass, up to the first
order in the finite conductivity correction, for two real metal semispaces
whose dielectric property is described by the plasma model. Application to the
Casimir effect in Randall-Sundrum spacetime is briefly discussed.Comment: 19 page
Exact Solutions of the Duffin Kemmer Petiau Equation for the Deformed Hulthen Potential
Using the Nikiforov Uvarov method, an application of the relativistic Duffin
Kemmer Petiau equation in the presence of a deformed Hulthen potential is
presented for spin zero particles. We derived the first order coupled
differential radial equations which enable the energy eigenvalues as well as
the full wavefunctions to be evaluated by using of the Nikiforov Uvarov method
that can be written in terms of the hypergeometric polynomials.Comment: 8 pages. submitted to Physica Script
Casimir effect of electromagnetic field in Randall-Sundrum spacetime
We study the finite temperature Casimir effect on a pair of parallel
perfectly conducting plates in Randall-Sundrum model without using scalar field
analogy. Two different ways of interpreting perfectly conducting conditions are
discussed. The conventional way that uses perfectly conducting condition
induced from 5D leads to three discrete mode corrections. This is very
different from the result obtained from imposing 4D perfectly conducting
conditions on the 4D massless and massive vector fields obtained by decomposing
the 5D electromagnetic field. The latter only contains two discrete mode
corrections, but it has a continuum mode correction that depends on the
thicknesses of the plates. It is shown that under both boundary conditions, the
corrections to the Casimir force make the Casimir force more attractive. The
correction under 4D perfectly conducting condition is always smaller than the
correction under the 5D induced perfectly conducting condition. These
statements are true at any temperature.Comment: 20 pages, 4 figure
Massive Electrodynamics and Magnetic Monopoles
Including torsion in the geometric framework of the Weyl-Dirac theory we
build up an action integral, and obtain from it a gauge covariant (in the Weyl
sense) general relativistic massive electrodynamics. Photons having an
arbitrary mass, electric, and magnetic currents (Dirac's monopole) coexist
within this theory. Assuming that the space-time is torsionless, taking the
photons mass zero, and turning to the Einstein gauge we obtain Maxwell's
electrodynamics.Comment: LaTex File, 9 pages, no figure
On the Weyl - Eddington - Einstein affine gravity in the context of modern cosmology
We propose new models of an `affine' theory of gravity in -dimensional
space-times with symmetric connections. They are based on ideas of Weyl,
Eddington and Einstein and, in particular, on Einstein's proposal to specify
the space - time geometry by use of the Hamilton principle. More specifically,
the connection coefficients are derived by varying a `geometric' Lagrangian
that is supposed to be an arbitrary function of the generalized (non-symmetric)
Ricci curvature tensor (and, possibly, of other fundamental tensors) expressed
in terms of the connection coefficients regarded as independent variables. In
addition to the standard Einstein gravity, such a theory predicts dark energy
(the cosmological constant, in the first approximation), a neutral massive (or,
tachyonic) vector field, and massive (or, tachyonic) scalar fields. These
fields couple only to gravity and may generate dark matter and/or inflation.
The masses (real or imaginary) have geometric origin and one cannot avoid their
appearance in any concrete model. Further details of the theory - such as the
nature of the vector and scalar fields that can describe massive particles,
tachyons, or even `phantoms' - depend on the concrete choice of the geometric
Lagrangian. In `natural' geometric theories, which are discussed here, dark
energy is also unavoidable. Main parameters - mass, cosmological constant,
possible dimensionless constants - cannot be predicted, but, in the framework
of modern `multiverse' ideology, this is rather a virtue than a drawback of the
theory. To better understand possible applications of the theory we discuss
some further extensions of the affine models and analyze in more detail
approximate (`physical') Lagrangians that can be applied to cosmology of the
early Universe.Comment: 15 pages; a few misprints corrected, one footnote removed and two
added, the formulae and results unchanged but the text somewhat edited, esp.
in Sections 4,5; the reference to the RFBR grant corrected
Green's functions and Hadamard parametrices for vector and tensor fields in general linear covariant gauges
We determine the retarded and advanced Green’s functions and Hadamard parametrices in curved spacetimes for linearized massive and massless gauge bosons and linearized Einstein gravity with a cosmological constant in general linear covariant gauges. These vector and tensor parametrices contain additional singular terms compared with their Feynman/de Donder-gauge counterpart. We also give explicit recursion relations for the Hadamard coefficients, and indicate their generalization to n dimensions. Furthermore, we express the divergence and trace of the vector and tensor Green’s functions in terms of derivatives of scalar and vector Green’s functions, and show how these relations appear as Ward identities in the free quantum theory
Dual equivalence in models with higher-order derivatives
We introduce a class of higher-order derivative models in (2,1) space-time
dimensions. The models are described by a vector field, and contain a
Proca-like mass term which prevents gauge invariance. We use the gauge
embedding procedure to generate another class of higher-order derivative
models, gauge-invariant and dual to the former class. We show that the results
are valid in arbitrary (d,1) space-time dimensions when one discards the
Chern-Simons and Chern-Simons-like terms. We also investigate duality at the
quantum level, and we show that it is preserved in the quantum scenario. Other
results include investigations concerning the gauge embedding approach when the
vector field couples with fermionic matter, and when one adds nonlinearity.Comment: RevTex4, 14 pages; new version includes duality at the quantum level,
and new references. To be published in J. Phys.
Kinematics and hydrodynamics of spinning particles
In the first part (Sections 1 and 2) of this paper --starting from the Pauli
current, in the ordinary tensorial language-- we obtain the decomposition of
the non-relativistic field velocity into two orthogonal parts: (i) the
"classical part, that is, the 3-velocity w = p/m OF the center-of-mass (CM),
and (ii) the so-called "quantum" part, that is, the 3-velocity V of the motion
IN the CM frame (namely, the internal "spin motion" or zitterbewegung). By
inserting such a complete, composite expression of the velocity into the
kinetic energy term of the non-relativistic classical (i.e., newtonian)
lagrangian, we straightforwardly get the appearance of the so-called "quantum
potential" associated, as it is known, with the Madelung fluid. This result
carries further evidence that the quantum behaviour of micro-systems can be
adirect consequence of the fundamental existence of spin. In the second part
(Sections 3 and 4), we fix our attention on the total 3-velocity v = w + V, it
being now necessary to pass to relativistic (classical) physics; and we show
that the proper time entering the definition of the four-velocity v^mu for
spinning particles has to be the proper time tau of the CM frame. Inserting the
correct Lorentz factor into the definition of v^mu leads to completely new
kinematical properties for v_mu v^mu. The important constraint p_mu v^mu = m,
identically true for scalar particles, but just assumed a priori in all
previous spinning particle theories, is herein derived in a self-consistent
way.Comment: LaTeX file; needs kapproc.st
The Mathematical Universe
I explore physics implications of the External Reality Hypothesis (ERH) that
there exists an external physical reality completely independent of us humans.
I argue that with a sufficiently broad definition of mathematics, it implies
the Mathematical Universe Hypothesis (MUH) that our physical world is an
abstract mathematical structure. I discuss various implications of the ERH and
MUH, ranging from standard physics topics like symmetries, irreducible
representations, units, free parameters, randomness and initial conditions to
broader issues like consciousness, parallel universes and Godel incompleteness.
I hypothesize that only computable and decidable (in Godel's sense) structures
exist, which alleviates the cosmological measure problem and help explain why
our physical laws appear so simple. I also comment on the intimate relation
between mathematical structures, computations, simulations and physical
systems.Comment: Replaced to match accepted Found. Phys. version, 31 pages, 5 figs;
more details at http://space.mit.edu/home/tegmark/toe.htm
Photon and Graviton Mass Limits
Efforts to place limits on deviations from canonical formulations of
electromagnetism and gravity have probed length scales increasing dramatically
over time.Historically, these studies have passed through three stages: (1)
Testing the power in the inverse-square laws of Newton and Coulomb, (2) Seeking
a nonzero value for the rest mass of photon or graviton, (3) Considering more
degrees of freedom, allowing mass while preserving explicit gauge or
general-coordinate invariance. Since our previous review the lower limit on the
photon Compton wavelength has improved by four orders of magnitude, to about
one astronomical unit, and rapid current progress in astronomy makes further
advance likely. For gravity there have been vigorous debates about even the
concept of graviton rest mass. Meanwhile there are striking observations of
astronomical motions that do not fit Einstein gravity with visible sources.
"Cold dark matter" (slow, invisible classical particles) fits well at large
scales. "Modified Newtonian dynamics" provides the best phenomenology at
galactic scales. Satisfying this phenomenology is a requirement if dark matter,
perhaps as invisible classical fields, could be correct here too. "Dark energy"
{\it might} be explained by a graviton-mass-like effect, with associated
Compton wavelength comparable to the radius of the visible universe. We
summarize significant mass limits in a table.Comment: 42 pages Revtex4. This version contains corrections and changes
contained in the published version, Rev. Mod. Phys. 82, 939-979 (2010), with
a few addition
- …