كوانتش نظريه ميدان اسكالر، فرميوني و الكترومغناطيس در مختصات مخروط نوري با استفاده از رهيافت هم تافته

چكيده انگليسي :

Light Cone Quantization of Scalar Fermionic and Electromagnetism field via Symplectic approach Hamed GhaemiDizicheh h ghaemi@ph iut ac ir 2012 3 12 Department of Physics Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language PersianSupervisor Dr A Shirzad shirzad@ipm irAbstractThe Light Cone coordinate was introduced as one of candidates for forms of dynamical variablesby Dirac in 1949 In this coordinate the time component of space time four vector at each point isperpendicular to the light cone surface Two other different coordinate forms have been introducedby Dirac Instant Form and Point Form Time component in Instant Form is chosen as usualas we use in ordinary physics and in Point Form time component is perpendicular to light conehyperboloid surface The Light Cone Coordinate also has application in different areas of physicssuch as nonperturbative QCD String theory Ads Cft etc As we will show in this thesis additionalsecond class constraints emerge within expressing field theory in light cone coordinate The Diracapproach in its ordinary framework helps us to quantize constraint system and find the commutationrelations among fields and momentum fields For this purpose we use Dirac bracket definition andfinally convert it to commutator By using this method in light cone quantization it can be depicted thatthe commutation relations among fields and momentum fields in this coordinate differ from ordinaryones For instance there is noncommutitativity between Scalar fields at equal light cone time Thisnoncommutitavity happens also in Fermionic and Electromagnetism field One indirect way tofind commutation relations among creation and annihilation operators in light cone quantization byDirac method is achieved by using commutation relations among fields and momentum fields In somemodels such as Fermionic Electromagnetism and Yang Mills theory in Light Cone coordinate we encounter a few number of constraint hence it makes some difficulties in computing the inverse ofthe constraint matrix We suggest Symplectic method to find commutation relations among creationand annihilation operators directly As we will see the quantization of field theory by this method ismore simple than Dirac method Symplectic approach applied in Light Cone Quantization in recentyears The Symplectic method that we use in this dissertation is based on Furrier expansion of fieldsand momentum fields in terms of Schrodinger modes By applying constraint relations the unphysicalmodes are removed and we can find the Dirac bracket of modes by means of Symplectic two form Byusing these Dirac brackets we can also find the commutation relations among fields and momentumfields These commutation relations are same as Dirac method Two other problems are also discussedin this thesis the physical modes and the propagator in Light Cone field theory Investigating thecovariance of the propagator helps us to find better the physical equivalence between different forms in our case the Light Cone and Instant forms In this thesis the Dirac and Symplectic approach are usedfor Scalar Fermionic and Electromagnetism field The propagator is also computed for Scalar and Fermionic field By applying the Symplectic approach it can be seen that extra constraints donot change the number of independent modes in three fields The propagator of Scalar and Fermionicfields in Light Cone coordinate is computed as same as propagator in ordinary coordinate Keywords Light Cone Coordinate Dirac approach Symplectic approach

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كوانتش نظريه ميدان اسكالر، فرميوني و الكترومغناطيس در مختصات مخروط نوري با استفاده از رهيافت هم تافته

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