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Manash Mukherjee

Publications and source records attributed to Manash Mukherjee.

7 recordsLinked to original sources
arXiv2008

Primitive Central Idempotents of the Group Algebra

An approach to representations of finite groups is presented without recourse to character theory. Considering the group algebra C[G] as an algebra of linear maps on C[G] (by left multiplication), we derive the primitive central idempotents as a simultaneous eigenbasis of the centre, Z(C[G]). We apply this framework to obtain the irreducible representations of a class of finite meta-abelian groups. In particular, we give a general construction of the isomorphism between simple blocks of C[G] and the corresponding matrix algebra where G can be any finite group.

math.RT↗
arXiv2003

A scalar invariant and the local geometry of a class of static spacetimes

The scalar invariant, I, constructed from the "square" of the first covariant derivative of the curvature tensor is used to probe the local geometry of static spacetimes which are also Einstein spaces. We obtain an explicit form of this invariant, exploiting the local warp-product structure of a 4-dimensional static spacetime, $~^{(3)}Σ\times_{f} \reals$, where $^{(3)}Σ$ is the Riemannian hypersurface orthogonal to a timelike Killing vector field with norm given by a positive function, $f$ on $^{(3)}Σ$. For a static spacetime which is an Einstein space, it is shown that the locally measurable scalar, I, contains a term which vanishes if and only if $^{(3)}Σ$ is conformally flat; also, the vanishing of this term implies (a) $~^{(3)}Σ$ is locally foliated by level surfaces of $f$, $^{(2)}S$, which are totally umbilic spaces of constant curvature, and (b) $^{(3)}Σ$ is locally a warp-product space. Futhermore, if $^{(3)}Σ$ is conformally flat it follows that every non-trivial static solution of the vacuum Einstein equation with a cosmological constant, is either Nariai-type or Kottler-type - the classes of spacetimes relevant to quantum aspects of gravity.

gr-qc↗
arXiv2002

Logarithmic corrections to finite size spectrum of SU(N) symmetric quantum chains

We consider SU(N) symmetric one dimensional quantum chains at finite temperature. For such systems the correlation lengths, ground state energy, and excited state energies are investigated in the framework of conformal field theory. The possibility of different types of excited states are discussed. Logarithmic corrections to the ground state energy and different types of excited states in the presence of a marginal opeartor, are calculated. Known results for SU(2) and SU(4) symmetric systems follow from our general formula.

cond-mat.str-el↗
arXiv1999

Domain Wall Spacetimes and Particle Motion

We present a mathematical framework for generating thick domain wall solutions to the coupled Einstein-scalar field equations which are (locally) plane symmetric. This approach leads naturally to two broad classes of wall-like solutions. The two classes include all previously known thick domain walls. Although one of these classes is static and the other dynamic, the corresponding Einstein-scalar equations share the same mathematical structure independent of the assumption of any reflection symmetry. We also exhibit a class of thick static domain wall spacetimes with different asymptotic vacua. Our analyses of particle motion in such spacetimes raises the interesting possibility that static domain walls will possess a unique experimental signature.

gr-qc↗
arXiv1997

Irrational Numbers of Constant Type --- A New Characterization

We obtain a new characterization for irrational numbers of constant type -- defined as irrationals with bounded partial quotients in their continued fraction expansion. The result is essential in the formulation of stability criteria for orbits of quantum twist maps in a class of dynamical systems.

math-ph↗
arXiv1997

Involutive Spacetime Distributions and p-Brane Dynamics

We propose a precise definition of multidimensional fluids generated by self-gravitating extended objects such as strings and membranes: a p-dimensional perfect fluid is a smooth involutive p-dimensional distribution on a spacetime, each integral manifold of which is a timelike, connected, immersed submanifold of dimension, p -- representing the history of a (p-1)-dimensional extended object. This geometric formulation of perfect fluids of higher dimensions naturally leads to the associated stress-energy tensor. Furthermore, the laws of temporal evolution and symmetries of such systems are derived, in general, from the Einstein field equations and the integrability conditions. We also present a matter model based on a 2-dimensional involutive distribution, and it is shown that the stress-energy tensor for self-gravitating strings gives rise to a non-trivial spherically symmetric spacetime with a naked singularity.

math-ph↗