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| Non-relativistic QED | |
|---|---|
| Name | Non-relativistic QED |
| Field | Quantum electrodynamics |
| Introduced | 20th century |
| Major figures | Paul Dirac, Richard Feynman, Sin-Itiro Tomonaga, Julian Schwinger, Hans Bethe, Pascual Jordan, Wolfgang Pauli, Lev Landau, Evgeny Lifshitz, John Bell, Freeman Dyson, Enrico Fermi, Werner Heisenberg, Erwin Schrödinger, Max Born, Niels Bohr, Arnold Sommerfeld, Vladimir Fock, Elliott Lieb, Barry Simon, I. M. Gelfand, Michael Reed, Peter Higgs, Anthony Leggett, Gerard 't Hooft, Stephen Hawking, David Gross, Frank Wilczek, Andrei Linde, Yoichiro Nambu, Ken Wilson, John Preskill, Alexei Abrikosov, Lev Gor'kov, Yakov Frenkel, Lars Onsager, Kirill Bogoliubov, Nikolay Bogolyubov, Wolfgang Ketterle, Eric Cornell, Carl Wieman, Serge Haroche, Claude Cohen-Tannoudji, Theodor W. Hänsch, William D. Phillips, John Townsend, Philip Anderson, Robert B. Laughlin, Roger Penrose |
Non-relativistic QED is the effective quantum field theory describing the interaction of non-relativistic charged particles with the quantized electromagnetic field. It provides a bridge between full relativistic quantum electrodynamics formulations and low-energy atomic, molecular, and condensed matter phenomena treated within frameworks associated with Paul Dirac, Erwin Schrödinger, Niels Bohr, and Arnold Sommerfeld. Historically developed through contributions by Richard Feynman, Julian Schwinger, and Sin-Itiro Tomonaga, the theory inherits operator methods and path-integral techniques connected to work by Werner Heisenberg, Max Born, and John Bell.
Non-relativistic QED arose as an adaptation of concepts from quantum electrodynamics and quantum mechanics to systems where particle velocities are small compared to the speed of light, building on mathematical frameworks advanced by Michael Reed and Barry Simon as well as renormalization insights from Hans Bethe and Ken Wilson. It plays a central role in analyses associated with Niels Bohr-type atomic models, Enrico Fermi's scattering theory, and precision spectroscopy pursued by groups led by Theodor W. Hänsch, Claude Cohen-Tannoudji, and Serge Haroche. Non-relativistic QED interfaces with approaches developed in the contexts of Landau and Lifshitz treatments of many-body systems and with conceptual advances due to John Bell and Freeman Dyson.
The canonical Hamiltonian formalism combines second-quantized matter operators and photon field operators similar to treatments by Paul Dirac and formal spectral analyses by Elliott Lieb and Barry Simon. One writes a Hamiltonian with kinetic terms parameterized by masses introduced in work by Lev Landau and coupling to vector potentials in gauges motivated by Wolfgang Pauli and Vladimir Fock. Rigorous existence and self-adjointness results draw on methods from I. M. Gelfand, Michael Reed, Barry Simon, and Elliott Lieb; spectral theorists such as Barry Simon and Elliott Lieb examine the essential spectrum and bound states using functional analytic tools developed in the tradition of John von Neumann and David Hilbert. Operator product expansions and commutation relations connect to algebraic methods associated with Pascual Jordan and Werner Heisenberg.
Non-relativistic QED underpins calculations for atomic spectra refined by Hans Bethe's early Lamb shift analysis, precision measurements undertaken by laboratories affiliated with Max Planck Society, CERN, and universities associated with Theodor W. Hänsch and William D. Phillips. It informs theory for trapped-ion experiments conducted by groups of Serge Haroche and David Wineland, and for cold-atom research led by Eric Cornell, Carl Wieman, and Wolfgang Ketterle. Applications extend to quantum optics paradigms shaped by Roy Glauber and Marlan Scully, to cavity QED experiments connected to Serge Haroche and Claude Cohen-Tannoudji, and to condensed matter phenomena discussed by Philip Anderson and Robert B. Laughlin. It also contributes to quantum chemistry methods developed in traditions of Linus Pauling and John Pople.
Perturbative expansions in the non-relativistic regime adapt Feynman diagrammatic methods from Richard Feynman and renormalized perturbation schema from Julian Schwinger and Sin-Itiro Tomonaga. Radiative corrections such as the Lamb shift and anomalous magnetic moments are computed using techniques elaborated by Hans Bethe, Gerard 't Hooft, and Kenneth G. Wilson; practical implementations rely on asymptotic analysis routines common in work by Elliott Lieb and Barry Simon. Connections to experimental tests involve collaborations or institutions like National Institute of Standards and Technology and groups inspired by Theodor W. Hänsch.
Renormalization in non-relativistic QED follows conceptual frameworks developed by Kenneth G. Wilson and mathematical clarification by Gerard 't Hooft, integrating effective field theory ideas influentialized by Steven Weinberg and John Preskill. Matching procedures to underlying relativistic quantum electrodynamics require counterterms and running parameters echoing analyses by Hans Bethe and Michael E. Peskin. Effective Hamiltonians used in atomic physics reflect operator product expansion philosophies connected to Alexander Polyakov and scaling methods from Ludwig Faddeev.
Bound-state problems exploit Schrödinger-based potentials corrected by radiative additions derived within non-relativistic QED; these corrections were historically central to Lamb shift work by Hans Bethe and continue in high-precision spectroscopy carried out by researchers at Max Planck Society and National Institute of Standards and Technology. Mathematical spectral analysis engages techniques from Elliott Lieb, Barry Simon, Michael Reed, and I. M. Gelfand; numerical and analytic approaches draw on perturbative spectral theory traditions associated with Kato, Tosio Kato, and John von Neumann.
Practical computations employ many-body and quantum chemistry algorithms inspired by John Pople, Walter Kohn, and Kieron Burke, as well as quantum optics simulation methods advanced by Roy Glauber and Marlan Scully. Techniques include variational methods traced to Erwin Schrödinger and Max Born, density functional-type approximations in the spirit of Walter Kohn, and diagrammatic Monte Carlo approaches linked to Nikolay Bogolyubov and Kirill Bogoliubov. Quantum simulation platforms developed in efforts by John Preskill and experimental programs at CERN and National Institute of Standards and Technology provide computational testing grounds. Advanced numerical linear algebra used in spectral solvers references contributions from Alan Turing and John von Neumann.