College of Liberal Arts & Sciences

# Math Physics Seminar

**Abstract:**

We Talk about stochastic quantization as a method to go from classical PDE with time parameter $\lambda$ to a corresponding quantum theory in the limit $\lambda\longrightarrow\infty$ Reflection positivity condition in relativistic quantum theory provides the connection from probability theory to quantum theory.In case of non-Gaussian

measure, d()[measure de ned over the Euclidean Schwartz distribution space $\delta\mu (\phi)$ [measure defined over the Euclidean Schwartz distribution space] is usually constructed as a weak limit of approximating measures that preserve reflection positivity which becomes problematic sometimes.We will discuss an alternative approach to obtain $\delta\mu (\phi)$ which is called stochastic quantization.This talk will be based on a result by Prof. Arthur Jaffe.[1]

[1] Arthur Jaffe. Quantum fields, stochastic pde, and reflection positivity. *arXiv preprint arXiv:1411.2964*, 2014.