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BINDING CONDITION OF THE MANY BODY SEMI-RELATIVISTIC PAULI-FIERZ MODEL (Applications of Renormalization Group Methods in Mathematical Sciences)

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BINDING CONDITION OF THE MANY BODY SEMI-RELATIVISTIC PAULI-FIERZ MODEL

ITARU SASAKI

DEPARTMENT OF MATHEMATICAL SCIENCES, SHINSHU UNIVERSITY, JAPAN

We consider the quantum system of$N$-relativistic particles interact with the

quan-tized electromagnetic field and the nuclear potential $V$. It is assumed that theparticles

have no spin and are obeyingthe Boltzmann statistics. If the ground stateof the total system $E^{V}(N)$ satisfy the inequality

$E^{V}(N)< \min\{E^{V}(N-M)+E^{0}(lII)|M=1, 2, . . . , N\}$, (1) then we say that the binding condition holds. We say that at least one particle is bound if the weaker condition

$E^{N}(N)<E^{0}(N)$ (2)

holds. To prove the condition (1) is important to prove the existence of the ground state. In this talk,

we

show that at least one particle is bound. The proofis

an

appli-cation of the functional integral representation of the semigroup of the Hamiltonian which is positivity preserving by the assumptions.

数理解析研究所講究録

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