Career Paul Dirac

1 career

1.1 gravity
1.2 quantum theory
1.3 dirac equation
1.4 magnetic monopoles
1.5 lucasian chair
1.6 professorship @ florida state university

career

dirac established general theory of quantum mechanics , discovered relativistic equation electron, bears name. remarkable notion of antiparticle each fermion particle – e.g. positron antiparticle electron – stems equation. first develop quantum field theory, underlies theoretical work on sub-atomic or elementary particles today, work fundamental our understanding of forces of nature. proposed , investigated concept of magnetic monopole, object not yet known empirically, means of bringing greater symmetry james clerk maxwell s equations of electromagnetism.

gravity

he quantised gravitational field, , developed general theory of quantum field theories dynamical constraints, forms basis of gauge theories , superstring theories of today. influence , importance of work has increased decades, , physicists use concepts , equations developed daily.

quantum theory

dirac s first step new quantum theory taken late in september 1925. ralph fowler, research supervisor, had received proof copy of exploratory paper werner heisenberg in framework of old quantum theory of bohr , sommerfeld. heisenberg leaned heavily on bohr s correspondence principle changed equations involved directly observable quantities, leading matrix formulation of quantum mechanics. fowler sent heisenberg s paper on dirac, on vacation in bristol, asking him paper carefully.

dirac s attention drawn mysterious mathematical relationship, @ first sight unintelligible, heisenberg had reached. several weeks later, in cambridge, dirac recognised mathematical form had same structure poisson brackets occur in classical dynamics of particle motion. thought developed quantum theory based on non-commuting dynamical variables. led him more profound , significant general formulation of quantum mechanics achieved other worker in field. dirac s formulation allowed him obtain quantisation rules in novel , more illuminating manner. work, published in 1926, dirac received phd cambridge. formed basis fermi-dirac statistics applies systems consisting of many identical spin 1/2 particles (i.e. obey pauli exclusion principle), e.g. electrons in solids , liquids, , importantly field of conduction in semi-conductors.

dirac famously not bothered issues of interpretation in quantum theory. in fact, in paper published in book in honour, wrote: interpretation of quantum mechanics has been dealt many authors, , not want discuss here. want deal more fundamental things.

the dirac equation

in 1928, building on 2×2 spin matrices purported have discovered independently of wolfgang pauli s work on non-relativistic spin systems (dirac told abraham pais, believe got these [matrices] independently of pauli , possibly pauli got these independently of me. ), proposed dirac equation relativistic equation of motion wave function of electron. work led dirac predict existence of positron, electron s antiparticle, interpreted in terms of came called dirac sea. positron observed carl anderson in 1932. dirac s equation contributed explaining origin of quantum spin relativistic phenomenon.

the necessity of fermions (matter) being created , destroyed in enrico fermi s 1934 theory of beta decay led reinterpretation of dirac s equation classical field equation point particle of spin ħ/2, subject quantisation conditions involving anti-commutators. reinterpreted, in 1934 werner heisenberg, (quantum) field equation accurately describing elementary matter particles – today quarks , leptons – dirac field equation central theoretical physics maxwell, yang–mills , einstein field equations. dirac regarded founder of quantum electrodynamics, being first use term. introduced idea of vacuum polarisation in 1930s. work key development of quantum mechanics next generation of theorists, in particular schwinger, feynman, sin-itiro tomonaga , dyson in formulation of quantum electrodynamics.

dirac s principles of quantum mechanics, published in 1930, landmark in history of science. became 1 of standard textbooks on subject , still used today. in book, dirac incorporated previous work of werner heisenberg on matrix mechanics , of erwin schrödinger on wave mechanics single mathematical formalism associates measurable quantities operators acting on hilbert space of vectors describe state of physical system. book introduced delta function. following 1939 article, included bra–ket notation in third edition of book, thereby contributing universal use nowadays.

magnetic monopoles

in 1931, dirac proposed existence of single magnetic monopole in universe suffice explain quantisation of electrical charge. in 1975, 1982, , 2009 intriguing results suggested possible detection of magnetic monopoles, there is, date, no direct evidence existence (see magnetic monopole#searches magnetic monopoles).

lucasian chair

dirac lucasian professor of mathematics @ cambridge 1932 1969. in 1937, proposed speculative cosmological model based on so-called large numbers hypothesis. during world war ii, conducted important theoretical , experimental research on uranium enrichment gas centrifuge.

dirac s quantum electrodynamics (qed) made predictions – more not – infinite , therefore unacceptable. workaround known renormalisation developed, dirac never accepted this. must dissatisfied situation , said in 1975, because so-called theory involve neglecting infinities appear in equations, neglecting them in arbitrary way. not sensible mathematics. sensible mathematics involves neglecting quantity when small – not neglecting because infinitely great , not want it! refusal accept renormalisation resulted in work on subject moving increasingly out of mainstream.

however, once rejected notes managed work on putting quantum electrodynamics on logical foundations based on hamiltonian formalism formulated. found rather novel way of deriving anomalous magnetic moment schwinger term , lamb shift, afresh in 1963, using heisenberg picture , without using joining method used weisskopf , french, , 2 pioneers of modern qed, schwinger , feynman. 2 years before tomonaga–schwinger–feynman qed given formal recognition award of nobel prize physics.

weisskopf , french (fw) first obtain correct result lamb shift , anomalous magnetic moment of electron. @ first fw results did not agree incorrect independent results of feynman , schwinger. 1963–1964 lectures dirac gave on quantum field theory @ yeshiva university published in 1966 belfer graduate school of science, monograph series number, 3. after having relocated florida near elder daughter, mary, dirac spent last fourteen years (of both life , physics research) @ university of miami in coral gables, florida, , florida state university in tallahassee, florida.

in 1950s in search better qed, paul dirac developed hamiltonian theory of constraints based on lectures delivered @ 1949 international mathematical congress in canada. dirac had solved problem of putting tomonaga–schwinger equation schrödinger representation , given explicit expressions scalar meson field (spin 0 pion or pseudoscalar meson), vector meson field (spin 1 rho meson), , electromagnetic field (spin 1 massless boson, photon).

the hamiltonian of constrained systems 1 of dirac s many masterpieces. powerful generalisation of hamiltonian theory remains valid curved spacetime. equations hamiltonian involve 6 degrees of freedom described




g

r
s




{\displaystyle g_{rs}}

,




p

r
s




{\displaystyle p^{rs}}

each point of surface on state considered.




g

m
0




{\displaystyle g_{m0}}

(m = 0, 1, 2, 3) appear in theory through variables




g

r
0




{\displaystyle g^{r0}}

,



(
−


g

00




)

−
1

/

2




{\displaystyle (-{g^{00}})^{-1/2}}

occur arbitrary coefficients in equations of motion. there 4 constraints or weak equations each point of surface




x

0




{\displaystyle x^{0}}

= constant. 3 of them




h

r




{\displaystyle h_{r}}

form 4 vector density in surface. fourth




h

l




{\displaystyle h_{l}}

3-dimensional scalar density in surface hl ≈ 0; hr ≈ 0 (r = 1, 2, 3)

in late 1950s, applied hamiltonian methods had developed cast einstein s general relativity in hamiltonian form , bring technical completion quantisation problem of gravitation , bring closer rest of physics according salam , dewitt. in 1959 gave invited talk on energy of gravitational field @ new york meeting of american physical society later published in 1959 phys rev lett 2, 368. in 1964 published lectures on quantum mechanics (london:academic) deals constrained dynamics of nonlinear dynamical systems including quantisation of curved spacetime. published paper entitled quantization of gravitational field in 1967 ictp/iaea trieste symposium on contemporary physics.

professorship @ florida state university

from september 1970 january 1971, dirac visiting professor @ florida state university in tallahassee. during time offered permanent position there, accepted, becoming full professor in 1972. contemporary accounts of time there describe happy except apparently found summer heat oppressive , liked escape cambridge.

he walk mile work each day , fond of swimming in 1 of 2 nearby lakes (silver lake , lost lake), , more sociable had been @ cambridge, worked @ home apart giving classes , seminars; @ fsu eat lunch colleagues before taking nap.

dirac published on 60 papers in last twelve years of life, including short book on general relativity. last paper (1984), entitled inadequacies of quantum field theory, contains final judgment on quantum field theory;

these rules of renormalisation give surprisingly, excessively agreement experiments. physicists these working rules are, therefore, correct. feel not adequate reason. because results happen in agreement observation not prove 1 s theory correct.

the paper ends these words;

have spent many years searching hamiltonian bring theory , have not yet found it. shall continue work on long can , other people, hope, follow along such lines.

(source: paul dirac: man , work abraham pais et al.)