Magnetic Order in Heisenberg Models on Non-Bravais Lattice: Popov-Fedotov Functional Method

We study magnetic properties of ordered phase in Heisenberg model on a non-Bravais lattice by means of Popov - Fedotov trick, which takes into account a rigorous constraint of a single occupancy. We derive magnetization and free energy using sadle point approximation in the functional integral formalism. We illustrate the application of the Popov -- Fedotov approach to the Heisenberg antiferromagnet on a honeycomb lattice.

Low-Temperature Spin Fluctuations beyond Spin Waves

A simple low-temperature dynamic spin-fluctuation theory of ferromagnetic metals is developed. The theory is based on the functional integral formalism for the multiband Hubbard Hamiltonian and takes into account both single-site and nonlocal spin fluctuations. We show that our approach correctly reproduces the T3/2 law at low temperatures. The calculated results of magnetic properties for Fe and Fe0.65Ni0.35 Invar demonstrate that the approach works on a much wider temperature interval than the spin-wave approximation.

An unified approach to inelastic light scattering in Keldysh–Schwinger functional integral formalism

We propose a theoretical framework which can treat the nonresonant and the resonant inelastic light scattering on an equal footing in the form of correlation function, employing Keldysh–Schwinger functional integral formalism. The interference between the nonresonant and the resonant process can be also incorporated in this framework. This approach is applied to the magnetic Raman scattering of two-dimensional antiferromagnetic insulators. The entire set of the scattering cross-sections are obtained at finite temperature, the result for the resonant part agrees with the one obtained by the conventional Fermi golden rule at zero temperature. The interference contribution is shown to be very sensitive to the scattering geometry and the band structure.

CANCELLATION OF ULTRA-VIOLET INFINITIES IN ONE LOOP GRAVITY

Quantization of gravity is a formidable challenge for modern theoretical physics. Ultraviolet divergencies are the problem. In 1974 the author used functional integral formalism for the quantization. The background formulation helped to solve the problem in one loop approximation. The author proved that the divergencies cancel on mass shell, because of Einstein's equations of motion.

The Metric Operator and the Functional Integral Formulation of Pseudo-Hermitian Quantum Mechanics

Pseudo-Hermitian quantum theories are those in which the Hamiltonian H satisfies H† = ηHη-1, where η = e-Q is a positive-definite Hermitian operator, rather than the usual H† = H. In the operator formulation of such theories the standard Hilbert-space metric must be modified by the inclusion of η in order to ensure their probabilistic interpretation. With possible generalizations to quantum field theory in mind, it is important to ask how the functional integral formalism for pseudo-Hermitian theories differs from that of standard theories. It turns out that here Q plays quite a different role, serving primarily to implement a canonical transformation of the variables. It does not appear explicitly in the expression for the vacuum generating functional. Instead, the relation to the Hermitian theory is encoded via the dependence of Z on the external source j(t). These points are illustrated and amplified in various versions of the Swanson model, a non-Hermitian transform of the simple harmonic oscillator.