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活动类型：学术报告

主讲人：夏道行院士

活动时间：

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Title: Determinant Formula and Trace formula for the Trace Class  Perturbation of Heisenberg Commutation Relation

Speaker: Daoxing Xia (夏道行)

Abstract: Suppose unbounded self-adjoint operators u and v satisfies the following condition:

 i(uv-vu)=I+D,where D is in the trace class and some other conditions. This relation between u and v is a trace class perturbation of Heisenberg commutation relation i(pq-qp)=h ,which is equivalent to the principal of uncertainty in quantum mechanics.

 

We give an integro-differential model of this pair of u and v.

The following determinant formula:

 Det(exp(if(u))exp(ig(v))exp(-if(u))exp(-ig(v+f ‘(u)))=exp(i(g(v+f ‘(u))-g (v))D)

is established, where f and g are in certain class of rational functions. Some  trace formula for this pair {u,v}is also given.

 

Besides,  an analytic model, some determinant formula and  trace formula for the unbounded operator u+iv are also established.