Quantum corrections to φ⁴ model solutions and applications to Heisenberg chain dynamics

The Heisenberg spin chain is considered in φ⁴ model approximation. Quantum corrections to classical solutions of the one-dimensional φ⁴ model within the correspondent physics are evaluated with account of rest d-1 dimensions of a d-dimensional theory. A quantization of the model is considered in terms of spacetime functional integral. The generalized zeta-function formalism is used to renormalize and evaluate the functional integral and quantum corrections to energy in a quasiclassical approximation. The results are applied to appropriate conditions of the spin chain model and its dynamics, for which elementary solutions, energy and the quantum corrections are calculated.