Abstract
We present path integral quantization of a massive superparticle in d =4 which preserves 1/4 of the target space supersymmetry with eight supercharges, and so corresponds to the partial breaking N = 8 to N = 2. Its worldline action contains a Wess-Zumino term, explicitly breaks d =4 Lorentz symmetry and exhibits one complex fermionic k-symmetry. We perform the Hamilton-Jacobi formalism of constrained systems, to obtain the equations of motion of the model as total differential equations in many variables. These equations of motion are in exact agreement with those obtained by Dirac’s method.
Highlights
The theory of constrained systems is a basis of modern physics: gauge field theories, quantum gravity, supergravity, string and superstring models are examples of systems with constraints
The path integral qantization of constrained systems is obtained for using the canonical path integral method, which based on the constrained Hamilton theory
The equations of motion are obtained as total differential equations in many variables, and the integrability conditions were shown to be equivalent to the vanishing of the variation of each H, i.e. dH 0 ’s, the system is integrable
Summary
The theory of constrained systems is a basis of modern physics: gauge field theories, quantum gravity, supergravity, string and superstring models are examples of systems with constraints. Step by step, using these primary constraints may generate more new inherent constraints, which are called Dirac secondary constraints. Such a way to calculate different constraints in Dirac formalism is named as Dirac-Bergmann algorithm, which was first proposed by Bergmann [6,7]. Canonical path integral method is a kind of quantization method [8,9], which depends on Hamilton-Jacobi formalism shown by Güler [10,11] This method has some very useful properties of obviating the need to distinguish primary and secondary constraints and the first and the second types of constraints. The method is simpler, and does not have such a hypothesis of Diracs conjecture, it has evoked much attention [12,13,14,15,16,17,18,19,20]
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