Nationality United States Fields Theoretical physics Name Erick Weinberg | Alma mater Harvard University Institutions Columbia University Doctoral advisor Sidney Coleman | |

Born August 29, 1947 (age 68)
Ossining, New York (1947-08-29) Doctoral students Kimyeong Lee Ai-qun Woo Bum-Hoon Lee Sang-Hoon Lee Nicholas Stathakis Yue Hu Hai Ren Dimitrios Metaxas Xingang Chen Huidong Guo James Hackworth Christopher Miller Adam Brown Ali Masoumi Hakjoon Lee Xiao Xiao Known for Coleman–Weinberg potential Lee–Weinberg–Yi metric Books Classical Solutions in Quantum Field Theory: Solitons and Instantons in High Energy Physics Education Harvard University, Manhattan College |

**Erick J. Weinberg** (born August 29, 1947) is a theoretical physicist and Professor of physics at the Department of Physics in Columbia University. Weinberg was educated at Manhattan College (BA 1968). He obtained a PhD from Harvard in 1973, under the supervision of Sidney Coleman with whom he discovered the Coleman–Weinberg mechanism for spontaneous symmetry breaking in quantum field theory. Professor Weinberg works on various branches in high-energy theory, including black holes, vortices, Chern–Simons theory, magnetic monopoles in gauge theories and cosmic inflation. Professor Weinberg also serves as the Editor of Physical Review D, as well as a visiting scholar of Korea Institute for Advanced Study (KIAS).

## Contents

- Academic career
- Notable Works
- Coleman–Weinberg potential
- Dimensional transmutation
- The graceful exit problem of old inflation
- Lee–Weinberg–Yi metric
- Selected articles and book
- References

## Academic career

Having graduated from Harvard University in 1973, Erick J. Weinberg went to the Institute for Advanced Study at Princeton as a postdoctoral researcher. At 1975, he was appointed by Columbia University as an assistant professor of physics. Promoted to professor of physics in 1987, Professor Weinberg has been a faculty member at Columbia University since then. From 2002 to 2006, Professor Weinberg served as the chair of Columbia University's physics department. Professor Weinberg is still actively researching BPS monopoles and vacuum decay.

## Notable Works

Professor Weinberg has worked on various branches in theoretical high energy physics, including the theory of spontaneous symmetry breaking, inflation,the theory of supersymmetric solitons, and the theory of vacuum decay via the nucleation of quantum/thermal bubbles.

## Coleman–Weinberg potential

Spontaneous symmetry breaking occurs in a theory when the state with lowest energy doesn't have as many symmetries as the theory itself, therefore one sees degenerate vacua connected by the quotient between the symmetry of the theory and the symmetry of the state, and the particle spectrum is classified by the symmetry group of the lowest energy state(vacuum). In the case that the quotient can be parametrized by continuous parameter(s), the local fluctuations of these parameters can be regarded as bosonic excitations (if the symmetry is bosonic), usually called Goldstone boson, which has profound implications. When coupled to gauge fields, these bosons mix into the longitudinal polarizations of the gauge fields and give masses to the fields, this is how Higgs mechanism works.

Usually the way to realize spontaneous symmetry breaking is to introduce a scalar field that has a tachyonic mass parameter, classically, then the classical vacuum is the solution that stays at the bottom of the potential, with the leading quantum contribution from the uncertainty principle, the vacuum can be viewed as a Gaussian wave packet around the lowest point of the potential.

The possibility that pointed out by Coleman and E.Weinberg is, even at the classical level one tunes the mass of the scalar field to be zero, quantum correction is able to modify the effective potential, turning the point that enjoys the whole symmetry of the theory from a local minima to a maxima, and generate new minima(vacuum) at configurations with less symmetry. Therefore spontaneous symmetry breaking can have a pure quantum origin.

Another important point about the mechanism is, the potential remains flat with the quantum correction, if we introduce appropriate counter-term to cancel the mass renormalization, with the minimum/maximum transition induced by a Log-like term.

Therefore it gives a natural arena for the idea of slow-roll inflation introduced by Linde, Albrecht and Steinhardt, which is still playing the dominant role among the theories of early universe.

## Dimensional transmutation

In the original paper of Coleman-Weinberg, as well as in the thesis of Erick Weinberg, Coleman and Weinberg discussed the renormalization of the couplings in various theories, and introduced the concept of "dimensional transmutation"---the running of coupling constants renders some coupling determined by an arbitrary energy scale, therefore although classically one starts from a theory in which there are several arbitrary dimensionless constants,one ends up with a theory with an arbitrary dimensionful parameter.

## The graceful exit problem of old inflation

In a paper with Alan Guth, Erick Weinberg discussed the possibility of ending the inflation with thermalization of vacuum bubbles.

The original proposal of inflation is, the exponentially growing phase ends via the nucleation of Coleman-de Luccia bubbles with a low vacuum energy, these bubbles collide and thermalize, leaving a homogeneous universe with high temperature. However, as the exponential growth of the near-de Sitter universe dilutes the bubbles nucleated, it is not obvious that the bubbles will really coalesse, in fact Guth and Weinberg proved the following statements:

The second statement suggests in a fixed coordinate any chosen bubble would be the largest in its own cluster, but this is a coordinate-dependent statement, after choosing the bubble, one can always find another coordinate in which there are bigger bubbles in the same cluster.

According to these statements, if the nucleation rate of bubbles is small, we will end up with bubbles that form clusters and will not collide with each other, with the heat release from vacuum decay stored in the domain-walls, quite different from what the hot Big-Bang starts from.

This problem called "graceful exit problem", discussed independently later by Hawking, Moss and Stewart, then solved by the proposal of new inflation by Linde, Abrecht and Steinhardt, which makes use of Coleman-Weinberg mechanism to generate the inflaton potential that satisfies slow-roll conditions.

## Lee–Weinberg–Yi metric

The existence of magnetic monopoles has long been an interesting and profound possibility. Such solitons could potentially explain the quantization of electric charge, as pointed out by Dirac; they can arise as the classical solutions in gauge theories, as pointed out by Polyakov and 't Hooft; and the inability to detect them is one of the motivations of proposing a period of inflation before the hot Big-Bang phase.

The dynamics of magnetic monopole solutions is especially simple when the theory is at BPS limit---when it can be extended to include fermionic sectors to form a supersymmetric theory. In these cases, the multi-monopole solutions can be explicitly obtained, the monopoles in a system are basically free because the interaction mediated by Higgs field is cancelled by the gauge interaction. in the case of a maximally broken gauge group into

Erick Weinberg, with Kimyeong Lee and Piljin Yi, did a calculation for the moduli space metric in the case of well-separated monopoles, with an arbitrary large compact gauge group

## Selected articles and book

*Physical Review D*.

**7**(6): 1888. Bibcode:1973PhRvD...7.1888C. doi:10.1103/PhysRevD.7.1888.

*Nuclear Physics B*.

**212**(2): 321–64. Bibcode:1983NuPhB.212..321G. doi:10.1016/0550-3213(83)90307-3.

*Physical Review Letters*.

**64**(19): 2234–2237. Bibcode:1990PhRvL..64.2234J. PMID 10041622. doi:10.1103/PhysRevLett.64.2234.

*Physical Review D*.

**54**(2): 1633. Bibcode:1996PhRvD..54.1633L. arXiv:hep-th/9602167 . doi:10.1103/PhysRevD.54.1633.

*Physics Reports*.

**438**(2–4): 65–236. Bibcode:2007PhR...438...65W. arXiv:hep-th/0609055 . doi:10.1016/j.physrep.2006.11.002.