Abstract
In Chaps. 2 and 5, we quantized mechanical systems and classical field theories via the functional integral formalism. Through a Wick rotation, we arrived at a (formal) Euclidean functional integral. In a next step, the underlying Euclidean spacetime is replaced by a lattice, and this discretization leads to well-defined lattice field theories—these are particular spin models with continuous target spaces. To calculate thermal expectation values, one imposes (anti)periodic boundary conditions in the imaginary time direction for the lattice fields. By these steps one approximates quantum field theories in d spacetime dimensions by particular classical statistical systems in d dimensions.
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Notes
- 1.
An elementary discussion of the subject can be found in [9].
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Wipf, A. (2021). Transfer Matrices, Correlation Inequalities, and Roots of Partition Functions. In: Statistical Approach to Quantum Field Theory. Lecture Notes in Physics, vol 992. Springer, Cham. https://doi.org/10.1007/978-3-030-83263-6_8
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