*Hans-Peter Eckle*

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780199678839
- eISBN:
- 9780191878589
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199678839.003.0012
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

This chapter extends the algebraic Bethe ansatz to the quantum Tavis–Cummings model, an N atom generalization of the Jaynes–Cummings model to describe the strong interaction between light and quantum ...
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This chapter extends the algebraic Bethe ansatz to the quantum Tavis–Cummings model, an N atom generalization of the Jaynes–Cummings model to describe the strong interaction between light and quantum matter. In the case of the quantum Tavis–Cum- mings model there is no underlying vertex model to suggest the constituent building blocks of the algebraic Bethe ansatz approach, e.g.like the L-matrix or ultimately the transfer matrix. The algebraic Bethe ansatz is then first applied to the Tavis–Cummings Hamiltonian with an added Stark term using a conjecture for the transfer matrix. The original Tavis–Cummings model and its algebraic Bethe ansatz are obtained in the limit of vanishing Stark term, which requires considerable care.Less

This chapter extends the algebraic Bethe ansatz to the quantum Tavis–Cummings model, an N atom generalization of the Jaynes–Cummings model to describe the strong interaction between light and quantum matter. In the case of the quantum Tavis–Cum- mings model there is no underlying vertex model to suggest the constituent building blocks of the algebraic Bethe ansatz approach, e.g.like the L-matrix or ultimately the transfer matrix. The algebraic Bethe ansatz is then first applied to the Tavis–Cummings Hamiltonian with an added Stark term using a conjecture for the transfer matrix. The original Tavis–Cummings model and its algebraic Bethe ansatz are obtained in the limit of vanishing Stark term, which requires considerable care.

*Jonathan Bain*

- Published in print:
- 2016
- Published Online:
- May 2016
- ISBN:
- 9780198728801
- eISBN:
- 9780191795541
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198728801.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

Chapter 2 seeks to understand the role that relativity plays in the CPT and spin–statistics theorems. It first considers the sense in which relativity is not sufficient for CPT invariance and the ...
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Chapter 2 seeks to understand the role that relativity plays in the CPT and spin–statistics theorems. It first considers the sense in which relativity is not sufficient for CPT invariance and the spin–statistics connection (SSC) by unraveling the different notions of locality (local commutativity, cluster decomposition, causality, and algebraic causality) that appear in these theorems on the one hand, and restricted Lorentz invariance on the other. It then considers the sense in which relativity is not necessary for CPT invariance and the SSC by unpacking the relations among restricted Lorentz invariance, modular covariance, and variants of the latter. The chapter ends by applying the existence problem of Chapter 1 to a critique of an influential claim that maintains that a violation of CPT invariance in an interacting relativistic quantum field theory entails a violation of Lorentz invariance.Less

Chapter 2 seeks to understand the role that relativity plays in the CPT and spin–statistics theorems. It first considers the sense in which relativity is not sufficient for CPT invariance and the spin–statistics connection (SSC) by unraveling the different notions of locality (local commutativity, cluster decomposition, causality, and algebraic causality) that appear in these theorems on the one hand, and restricted Lorentz invariance on the other. It then considers the sense in which relativity is not necessary for CPT invariance and the SSC by unpacking the relations among restricted Lorentz invariance, modular covariance, and variants of the latter. The chapter ends by applying the existence problem of Chapter 1 to a critique of an influential claim that maintains that a violation of CPT invariance in an interacting relativistic quantum field theory entails a violation of Lorentz invariance.