A correspondence between the free and interacting field

The European Physical Journal C, vol. 83

Abstract

Abstract We discover a correspondence between the free field and the interacting states. This correspondence is firstly given from the fact that the free propagator can be converted into a tower of propagators for massive states, when expanded with the Hermite function basis. The equivalence of propagators reveals that in this particular case the duality can naturally be regarded as the equivalence of one theory on the plane wave basis to the other on the Hermite function basis. More generally, the Hermite function basis provides an alternative quantization process with the creation/annihilation operators that correspond directly to the interacting fields. As an illustration, we apply this basis to the $$3+1$$ 3 + 1 dimensional Yang–Mills theory, where the three-dimensional space being reduced through the Hermite function basis, and an auxiliary parameter $$\omega $$ ω denotes for string tension. At large $$\omega $$ ω limit, with then considering only the lowest order Hermite function (Lowest Landau Level), the equivalent action becomes the Banks–Fischler–Shenker–Susskind (BFSS) matrix model. At small $$\omega $$ ω limit, the perturbative series summed over all orders of Hermite function gives a massive gluon propagator.

Authors 4

1. Fei Gao

   Peking University

   Affiliation as printed

   Center for High Energy Physics, Peking University, Beijing, 100871, China

   Center for High Energy Physics, Peking University, Beijing, China

2. Minghui Ding corresponding

   Helmholtz-Zentrum Dresden-Rossendorf

   Affiliation as printed

   Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328, Dresden, Germany

   Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany

3. Yu‐xin Liu

   Peking University · Collaborative Innovation Center of Quantum Matter · State Key Laboratory of Nuclear Physics and Technology

   Affiliation as printed

   Center for High Energy Physics, Peking University, Beijing, 100871, China

   Collaborative Innovation Center of Quantum Matter, Beijing, 100871, China

   Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, 100871, China

   Center for High Energy Physics, Peking University, Beijing, China

   Collaborative Innovation Center of Quantum Matter, Beijing, China

   Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China

4. Sebastian M. Schmidt Aachen III. Physikalisches Institut B

   Helmholtz-Zentrum Dresden-Rossendorf · RWTH Aachen University

   Affiliation as printed

   Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328, Dresden, Germany

   RWTH Aachen University, III. Physikalisches Institut B, 52074, Aachen, Germany

   Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany

   RWTH Aachen University, Aachen, Germany