随机过程在量子场论计算中的应用（Applications of stochastic processes in quantum field theory）.docVIP

随机过程在量子场论计算中的应用（Applications of stochastic processes in quantum field theory） Applications of stochastic processes in quantum field theory Wen / LIN The so-called stochastic process, refers to under certain conditions, may or may not occur, the process of uncertainty, that is: with probability. The mathematical model of the most common stochastic process is the random walk (random, walk). The well-known phenomenon of Browns motion can be explained by random walks. One of the most important physical quantities in random walk is the probability distribution function. It is the probability of a particle appearing at the initial moment at the origin and following the random walk of N steps. In the random walk model, we assume that the particle is the same size and takes the same time each walk, so the N in the middle is equivalent to the time variable. Through the consideration of conditional probabilities and Fu Liye transform technique, we can derive the path integral representation of the time evolution operator in quantum mechanics and its form (also known as the propagator) the integral expression of the same Feynman path in mathematics, there is a one-to-one correspondence [1]. This correspondence is also physically meaningful because a quantum system has quantum uncertainty and, therefore, has randomness. The Feynman path integral representation of quantum mechanics can express this randomness explicitly. We can each path path integral propagator in quantum system is regarded as a random process, the weight of the propagator contribution is the role of classical mechanical systems corresponding to S for a quantum system of quantity, so in the kinetic minus potential item. If it goes through a Wick rotation: , Time will be converted to virtual time after t(so on the tau is still taking real values), can be transformed into complete and random walk the path integral is one-to-one form. In this form, the factor becomes, where SE is the kinetic energy of the correspo