Diagonalizing the Hamiltonian of $\lambda \phi^4$ Theory in 2 Space-Time Dimensions
Abstract
We propose a new non-perturbative technique for calculating the field-theory S-matrix directly from the eigenstates of the Hamiltonian. Our method involves a discretized momentum space and a momentum cutoff, thereby truncating the Hilbert space and making numerical diagonalization of the Hamiltonian achievable. We show how to do this in the context of a simplified $\lambda \phi^4$ theory in two space-time dimensions. We present the results of our diagonalization, its dependence on time, its dependence on the parameters of the theory and its renormalization.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2016
- DOI:
- 10.48550/arXiv.1603.01273
- arXiv:
- arXiv:1603.01273
- Bibcode:
- 2016arXiv160301273C
- Keywords:
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- High Energy Physics - Phenomenology;
- High Energy Physics - Lattice
- E-Print:
- 27 pages, 20 figures