UVA Physics-新东方前途出国

Mathematical Physics

Overview

Physics and mathematics have always been closely intertwined, with developments in one field frequently inspiring the other. Currently, there are many unsolved problems in physics which will likely require new innovations in mathematical physics.

For example, theoretical physicists have used field theory to successfully describe the strong and electroweak interactions of particle physics, and all sorts of condensed matter physics. Most of our understanding has been based on perturbative calculations, valid when coupling constants are small. Nevertheless, we believe that quantum field theories describe subatomic physics even when couplings are large; for example, gauge theory should still describe the physics of confinement, which by its nature requires strong couplings. Moreover, experimental advances have allowed extensive scrutiny of condensed matter systems like the quantum Hall effect, quantum impurities and spin chains where the interactions are strong. Such systems often exhibit non-Fermi-liquid behavior, where perturbation theory around free electrons cannot even be formulated.

Because perturbation theory is not useful for such problems, it is vital that new methods of understanding strong-coupling physics be developed. A number of such methods are under investigation at UVa. The Bethe Ansatz allows many two-dimensional models to be solved; for example, in the fractional quantum Hall effect, the point-contact tunneling amplitude was recently exactly computed. A symmetry between bosons and fermions called supersymmetry often yields exact results in any dimension. Recently, remarkable dualities between theories at weak coupling and those at strong coupling have been discovered. These and other methods are being developed further to provide not only new types of mathematics, but to describe the physical world.

What You Might Do with a Physics MajorI  think  a  good  general  answer  is  that  for  students  who  enjoy  physics,  a  physics  major  is  very  stimulating  and  intellectually  rewarding,  and  it  is  good  preparation  for  a  remarkable  variety  of  careers.  Indeed, the analytical and problem solving skills learned in studying physics can be even more important in the future than the specific scientific knowledge. This is a message we get from a large number of our physics  majors.  Even  those  whose  jobs  have  little  to  do  with  physics  feel  that  these  skills  learned  in  physics complemented their courses in the humanities and social sciences to such an extent that they still regard their physics major as their best choice.Some similar facts about the skills physics graduates find most useful emerged from a survey by the American Institute of Physics. They queried some thousands of people with physics degrees (bachelor’s, master’s, and doctorate) working in industry, government, and secondary and higher education about the skills they used most frequently. At all degree levels and for all types of jobs, whether directly involving physics or not, almost 100% of respondents said that problem solving is their most frequently used skill (https://www.aip.org/statistics/data-graphics/knowledge-and-skills-regularly-used-physics-bachelor%E2%80%99s-employed-private). Computer skills were highly ranked by most of the respondents. Even more highly ranked were interpersonal skills and technical writing. These same skills have been identified as most important by many companies who hire physics graduates. Physics majors are very successful in getting into law school or medical school (https://www.aip.org/statistics/reports/mcat-lsat-and-physics-bachelors). We  are  addressing  the  development  of  these  skills  explicitly  in  the  physics  major.  Problem  solving  and  computing  are  strong  components  of  the  program.  The  upper-level physics laboratories and independent study courses are structured to provide excellent opportunities for developing skills in both oral and written communication of technical material. Spontaneous teamwork on solving problems in the upper-level courses has long been a part of being a physics major. Working with a variety of partners in the  lab  courses  and  research  groups  also  helps  develop  skills  in  interpersonal  relationships.  These  experiences are being supplemented in some physics classes by group problem solving, which has been shown  to  be  an  effective  way  of  learning  new  concepts  and  has  the  added  effect  of  teaching  and  encouraging teamwork.