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Lectures on Quantum Mechanics and Relativistic Field Theory by P. A.M. Dirac (18-Jul-2012) Paperback
2012 Reprint of 1955 Edition. Exact facsimile of the original edition, not reproduced with Optical Recognition Software. Dirac is widely regarded as one of the world's greatest physicists. He was one of the founders of quantum mechanics and quantum electrodynamics. His early contributions include the modern operator calculus for quantum mechanics, which he called transformation theory, and an early version of the path integral. His relativistic wave equation for the electron was the first successful attack on the problem of relativistic quantum mechanics. Dirac founded quantum field theory with his reinterpretation of the Dirac equation as a many-body equation, which predicted the existence of antimatter and matter-antimatter annihilation. He was the first to formulate quantum electrodynamics, although he could not calculate arbitrary quantities because the short distance limit requires renormalization. Dirac discovered the magnetic monopole solutions, the first topological configuration in physics, and used them to give the modern explanation of charge quantization. He developed constrained quantization in the 1960s, identifying the general quantum rules for arbitrary classical systems. These lectures were given delivered and published during his tenure at Princeton's Institute for Advanced Study in the 1930's.
- GenresPhysics
Unknown Binding
First published July 18, 2012
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June 24, 2024
A SERIES OF DETAILED, TECHNICAL LECTURES
Paul Adrien Maurice Dirac (1902-1984) was an English theoretical physicist who shared the 1933 Nobel Prize in Physics with Erwin Schrödinger.
In the first lecture, he wrote, “In classical mechanics the state of a given system can be defined by giving the positions and momenta of the particles constituting it at a given time. In quantum mechanics one cannot specify a state in the same way since one cannot determine all the dynamical variables of the system at a given time. A state in quantum mechanics is determined by specifying the values of as many dynamical variables as the theory allows one to specify simultaneously, at given time. The ugly feature of indeterminacy of the results of observation on a system is compensated by the principle of superposition of states which will now be introduced. Consider the set of all the states of a dynamical system. The principle of superposition allows one to superpose any to states to get other states belonging to the set. This property of the states makes it convenient to represent them by vector in a vector space.” (Pg. 1-2)
In Lecture 11, he notes, “It is seen that the formal structure of quantum theory is intimately connected with that of classical mechanics. This makes it seem impossible to change quantum mechanics in any way without spoiling the entire scheme. To make progress at the present day, instead of trying any such changes one should concentrate on obtaining better Hamiltonians. The difficulties encountered in present-day theories of elementary particles may be entirely due to people working with the wrong Hamiltonians.” (Pg. 77)
He argues in Lecture 13, “There is a general rule that particles of half-odd-integral spins are fermions and those of integral spins are bosons. This rule is self-consistent. For consider two particles of spin ½h each. The combined system consisting of both of them bound together will have integral spin, and a wave function describing an assembly of them will be separate. The rule has not been strictly proved, although it is much easier to construct relativistic theories of particles conforming to it than disobeying it, It has to be taken as an empirical result.” (Pg. 95)
He adds, “In the work of finding the Hamiltonian we are guided by classical mechanics. When dealing with spin we cannot rely on classical mechanics, for the classical mechanical concept of spin is inadequate. But we can invoke the principle of relativity for the purpose. It is necessary that an accurate theory should conform to the principle of relativity. This imposes severe restrictions in our search for a Hamiltonian It requires us usually to have interactions only through the intermediary of fields. One can have relativistic interactions at a distance in special cases, but these cases need a complicated transformation to show their relativistic invariance.” (Pg. 97-98)
He begins Lecture 14 with the statement, “The laws of quantum mechanics must be so formulated that they satisfy the principle of special relativity, i.e. they must be the same for two observers in uniform relative motion. This requirement becomes important when dealing with particles whose velocities are near that of light. It is not important to make the laws of quantum mechanics obey the principle of general relativity, since the latter is needed only to explain gravitational effects, which are extremely small for atomic systems.” (Pg. 99)
He concludes the final lecture with the statement, “It is probable that the source of this difficulty is that we are using the wrong Hamiltonian. There is no compelling argument in favor of it and it is worth while trying to find a better one. In the present theory one can give a meaning to the electron without the coulomb field. The quantity [w] by itself refers to such an electron. Probably in a correct theory it should be impossible to conceive of an electron without the accompanying coulomb field. One possibility in this direction is to regard, classically, an electron as the end of a single Faraday line of force. The electric field in this picture is built up from discrete Faraday lines of force, which are to be treated as physical things, like strings. One has then to develop a dynamic for such a string-like structure, and quantize it. The lack of spherical symmetry of this classical model of the electron gets removed by quantization. In such a theory a bare electron would be inconceivable, since one cannot imagine the end of a piece of string without having the string.” (Pg. 166)
This VERY technical book is written for those very familiar with the field.
Paul Adrien Maurice Dirac (1902-1984) was an English theoretical physicist who shared the 1933 Nobel Prize in Physics with Erwin Schrödinger.
In the first lecture, he wrote, “In classical mechanics the state of a given system can be defined by giving the positions and momenta of the particles constituting it at a given time. In quantum mechanics one cannot specify a state in the same way since one cannot determine all the dynamical variables of the system at a given time. A state in quantum mechanics is determined by specifying the values of as many dynamical variables as the theory allows one to specify simultaneously, at given time. The ugly feature of indeterminacy of the results of observation on a system is compensated by the principle of superposition of states which will now be introduced. Consider the set of all the states of a dynamical system. The principle of superposition allows one to superpose any to states to get other states belonging to the set. This property of the states makes it convenient to represent them by vector in a vector space.” (Pg. 1-2)
In Lecture 11, he notes, “It is seen that the formal structure of quantum theory is intimately connected with that of classical mechanics. This makes it seem impossible to change quantum mechanics in any way without spoiling the entire scheme. To make progress at the present day, instead of trying any such changes one should concentrate on obtaining better Hamiltonians. The difficulties encountered in present-day theories of elementary particles may be entirely due to people working with the wrong Hamiltonians.” (Pg. 77)
He argues in Lecture 13, “There is a general rule that particles of half-odd-integral spins are fermions and those of integral spins are bosons. This rule is self-consistent. For consider two particles of spin ½h each. The combined system consisting of both of them bound together will have integral spin, and a wave function describing an assembly of them will be separate. The rule has not been strictly proved, although it is much easier to construct relativistic theories of particles conforming to it than disobeying it, It has to be taken as an empirical result.” (Pg. 95)
He adds, “In the work of finding the Hamiltonian we are guided by classical mechanics. When dealing with spin we cannot rely on classical mechanics, for the classical mechanical concept of spin is inadequate. But we can invoke the principle of relativity for the purpose. It is necessary that an accurate theory should conform to the principle of relativity. This imposes severe restrictions in our search for a Hamiltonian It requires us usually to have interactions only through the intermediary of fields. One can have relativistic interactions at a distance in special cases, but these cases need a complicated transformation to show their relativistic invariance.” (Pg. 97-98)
He begins Lecture 14 with the statement, “The laws of quantum mechanics must be so formulated that they satisfy the principle of special relativity, i.e. they must be the same for two observers in uniform relative motion. This requirement becomes important when dealing with particles whose velocities are near that of light. It is not important to make the laws of quantum mechanics obey the principle of general relativity, since the latter is needed only to explain gravitational effects, which are extremely small for atomic systems.” (Pg. 99)
He concludes the final lecture with the statement, “It is probable that the source of this difficulty is that we are using the wrong Hamiltonian. There is no compelling argument in favor of it and it is worth while trying to find a better one. In the present theory one can give a meaning to the electron without the coulomb field. The quantity [w] by itself refers to such an electron. Probably in a correct theory it should be impossible to conceive of an electron without the accompanying coulomb field. One possibility in this direction is to regard, classically, an electron as the end of a single Faraday line of force. The electric field in this picture is built up from discrete Faraday lines of force, which are to be treated as physical things, like strings. One has then to develop a dynamic for such a string-like structure, and quantize it. The lack of spherical symmetry of this classical model of the electron gets removed by quantization. In such a theory a bare electron would be inconceivable, since one cannot imagine the end of a piece of string without having the string.” (Pg. 166)
This VERY technical book is written for those very familiar with the field.
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