Abstract
In this chapter the Pauli–Fierz model in non-relativistic quantum electrodynamics is studied. This model describes the minimal interaction between quantum matters (electrons) and a massless quantized radiation field (photons). The existence of the ground state of the Pauli–Fierz Hamiltonian is proven.
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- 1.
Suppose \(f(x)\in C_0^\infty ({{\mathbb R}^d})\). Then there exists a function \(F(z)\in C_0^\infty ({\mathbb C})\) such that (1) \(F(x)=f(x)\) for \(x\in {{\mathbb R}^d}\), (2) \(|\partial _{\bar{z}} F(z)|\le C_n|\mathfrak {I}z|^n\) for any \(n\in {\mathbb N}\), (3) \(f(A)=\frac{1}{\pi }\int _{{\mathbb C}}\partial _{\bar{z}}F(z) (A-z)^{-1}dxdy\), where \(\partial _{\bar{z}}=\partial _x+i\partial _y\). The integral is defined in the uniform operator topology. F is called almost analytic extension of f. We refer to see [26].
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© 2019 The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd.
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Hiroshima, F. (2019). The Pauli–Fierz Model. In: Ground States of Quantum Field Models. SpringerBriefs in Mathematical Physics, vol 35. Springer, Singapore. https://doi.org/10.1007/978-981-32-9305-2_3
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DOI: https://doi.org/10.1007/978-981-32-9305-2_3
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