TAILIEUCHUNG - Báo cáo " PATH INTEGRAL QUANTIZATION OF SELF INTERACTING SCALAR FIELD WITH HIGHER DERIVATIVES "

Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their time derivatives are considered as independent canonical variables. Consequently, generating functional, explicit expressions of propagators and Feynman diagrams in φ3 theory are found. | PATH INTEGRAL QUANTIZATION OF SELF INTERACTING SCALAR FIELD WITH HIGHER DERIVATIVES Nguyen Duc Minh1 Department of Physics College of Science Vietnam National University Hanoi Abstract Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their time derivatives are considered as independent canonical variables. Consequently generating functional explicit expressions of propagators and Feynman diagrams in f 3 theory are found. PACS number . 1. INTRODUCTION Field systems containing derivatives of order higher than first have more and more important roles with the advent of super-symmetry and string theories 1 . However up to now path integral quantization method is almost restricted to fields with first derivatives 2 3 4 . The purpose of this paper is to apply the new ideal velocities have to be taken as independent canonical variables 5 to extending the method to self-interacting scalar field containing higher derivatives. The paper is organized as follows Section II presents the application of this quantization method to quantizing free scalar field . Section III is devoted to studying the Feynman diagrams of self-interacting scalar field. Section IV is for the drawn conclusion. 2. FREE SCALAR FIELD Let us consider Lagrangian density for a free scalar field containing second order derivatives L 1 dfi cHfi m2 fi2 2A_ fi fi 1 where is D Alamber operator ỠM ỠM dfl A A is Laplacian and A is a parameter with dimension of mass. It will give a term with k4 in the denominator of the corresponding Feynman propagator. This renders a finite result for some diagrams and consequently it may permit the introduction of convenient counter-terms to absorb the 1 email nguyenducminh3_1@ 1 2 Nguyen Duc Minh infinities which will appear when the limit A is taken. The canonical momenta conjugate to ộ and ộ are .

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