# Research Contents

## QFT vs QM

Quantum theory is the dynamical law in the world of atoms, electrons, nuclei and elementary particles.

There are two different quantum theories, namely, quantum mechanics and quantum field theory.

Although both tend to be identified for the reason that the second quantized version of many body quantum mechanics gives the quantum field theoretical formulation,

quantum field theory has a much wider scope and is the most fundamental dynamical law: it is consistent with special relativity and describe the creation- and annihilation-processes of particle, and its applications to various phenomena in particle and nuclear physics, cosmology and condensed matter physics have been successful.

But it is far from being completed, and is to be pursued further.

Our central aim of research is to elucidate quantum field theory at a deeper level and to extend its applications.

## Thermal Field Theory

We analyze the systems under thermal situations, using the methods of thermodynamics and statistical physics,

whether the dynamics is Newton’s mechanics or quantum mechanics.

But when the dynamics is quantum field theory,

the theory for systems under thermal situations is not established yet.

We aim to construct thermal field theory to deal with systems of quantum field under thermal situations,

in particular in nonequilibrium, using the formulation of Thermo Field Dynamics.

## Systems of Cold Neutral Atoms

Since the Bose-Einstein condensates of neutral atoms in the trap potential at the order of μK or below were realized in 1995, systems of cold neutral atoms have been attracting much attention. The systems of trapped cold neutral atoms give us opportunities to test quantum many-body theories, i.e., quantum field theory and thermal field theory (equilibrium and nonequilibrium). This is firstly because they are dilute and weak-interacting systems so that theoretical calculations can be compared directly with experimental results. The second reason is that many experimental parameters, e.g., number of atoms, temperature, coupling constant of atomic interaction, strength and form of trapping potential, external disturbance and so on, can be changed in a controlled way so that various interesting experimental situations can be realized. We therefore analyze the systems in the languages of quantum field theory and thermal field theory.

## Foundations of Quantum Theory

It is true that the applications of quantum theory to phenomena in a microscopic world lead to correct results. But quantum theory itself is not easy to understand, above all the introduction of probabilistic interpretation. In order to get a deeper insight into quantum theory, we should view it from all angles. We are interested in the researches concerning to foundations of quantum theory.

## Our Recent Research Subjects

- We formulate nonequilibrium Thermo Field Dynamics for the systems of trapped cold neutral atoms, and derive the kinetic equations (quantum Boltzmann equations) and investigate their implications.
- We study the phase structure (superfluid- Mott insulator phases) of systems of cold neutral atoms in optical lattice.
- As a research on the foundation of quantum theory, we take Nelson’s stochastic quantization method.