Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


Physics and Applied Mathematics Unit (PAMU-Kolkata)


Bandyopadhyay, Pratul (PAMU-Kolkata; ISI)

Abstract (Summary of the Work)

A now fornulation of the problen of junotion condiiions 1a given, It is pointed out that, if the existing the ory of relativity ie to be consistent with the existence of natter in the form of particles, thon the cannot be continuously aifferentiable everywhere, The mathonatical part of the problem of Junction conditiona is solved by using nonatandard analysis to define prod uo ta and compoaitions vith distributiona, The definitiona are auch that o ontimaed belief in the equations of relativity is justified, As an application, the equations of IRotion for the apherically-synne tric surface layor, at the Schwerzachild-Minkowsici junction, are derived, The se agree with the equationa dorivod by earlier authors in being under- determined, Appliontions to singularity theory are pointed out,.II A RELATIVISTIC MODEL OP THE EIECTRON The problem of the notion of surface layors in rela- tivity is considered in its most genoral forn using the techniques developed in the carlier chapter, By using generalcoordina te trenaf orna tiona it la shown that tho equationa of notion aro nanifestly underdeternined, This indeteamimay can bo overcone by preseribing an equation of state, in the nacroscopic DR e. It is coneluded that surfaee lnyers, in the nicroscopic cane, onn evolve in an essentially arbitrery manner, and that it is poBeiblo to conatruct shell-1ilo nodels of elementary charged particles aatiafying the restrictiona in Chaptor IV.II IMIERPRETATION OP THE INDETERHINACY RELATIONS It is pointed out that, vithin tho axiona tic f ormula. tion of quantum mechanics, the precise form of tho indoter- ninacy relations introducea scne qualitatively new features. As a result, the notion of aimultano ous aeaauramunt, which is an intogral part of the ununl interpretation of the indetorminaey relationa, bec omes rodundant and nisleading. It ia ahovn that the preciao form, of the indeterninnoy relationa, na cesaarily loada to the conclusion that the parti- clea described by quantum nechaniea hsve some fini te (as oppoaed to infinitesinal) spatial oxtenaion.INTBRPRETATION OF QUANTUM NECHANICS AS A PIECRY OP EXTENDED PAT ICLES Developing on the conelusions roached in the previous cha pter, it is proposed to intoryret quantum mechanies ns a theory of extended particles, Cortain restrictions aro placed on the unierlying model for extended partielos, Wvo-perticlo duality is interproted in the context of the pulaationo of the partielo. Tho Mavofunction is relatud to the (renl an) exten- aion of tho particlo, It is ahown that thia vivef uno tion satiafies the Schrodinger oquation, In this the ory, the peouliarities of quantum probabilities sre related to the asoumption that the particle is shell-1ike, It ia ahown that a ropresentation of dynamical variablas by positive-operator valued meaatres ia possible, The enpirical prodictions of thia the ory are pointed out, along with some unsolvod problema, It is concluded that it is, at least partially, posalblc to interpret quantım mochanics as a saniclassionl deseription of the dyaamios of extendod partielea, If this interprotation is correct, quantun nechenica would fail at very high ener- gioa, and, possibly, at very low energics.


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