Hall 123

Invariant ultraviolet scale correction to photon dynamics, degenerate Fermi gas and its possible implications

Dheeraj Kumar Mishra

IMSc

We consider the invariant ultraviolet scale modied/deformed Poincare
algebra proposed by Magueijo and Smolin and study the possible implica-
tions to the known physics. We get such a scale modied dispersion rela-
tion and an eective invariant ultraviolet energy cut-o. We study various
equilibrium thermodynamic properties of blackbody radiation (i.e. a pho-
ton gas) and degenerate fermions with such modications. The energy
density, specic heat etc. of the photon gas follows the usual acoustic
phonon dynamics as have been well studied by Debye. Other modied
thermodynamic quantities like pressure, entropy etc. also get the correc-
tion. The usual Stefan-Boltzmann law gets modied. The invariant scale
can be taken as Planck scale and Planck scale acts as a threshold where
a new description of spacetime is expected to appear. The phase-space
measure is also expected to get modied for an exotic spacetime appearing
at Planck scale, which in turn leads to the modication of Planck energy
density distribution and the Wien's displacement law. We also found that
the non-perturbative nature of the thermodynamic quantities in the SR
limit (for both the case with ultraviolet cut-o and the modied measure
case), due to nonanalyticity of the leading term, is a general feature of the
theory accompanied with an ultraviolet energy cut-o. We also study the
modied thermodynamics of the degenerate Fermi gas. As an example we
explore the dynamics of the compact stellar object such as white dwarf by
nding the modied degenerate pressure and the modied Chandrasekhar
limit.