Quantum mechanics is one of the most fascinating， and at the same time most controversial， branches of contemporary science. Disputes have accompanied this science since its birth and have not ceased to this day. What is the sense of a probability interpretation of a physical phenomenon? Which approach to a quantum field theory is more consistent? How must we comprehend a quantum world? This book，leaving aside the search for spiritual content and answers to these questions， allows one to deeply contemplate some ideas and methods that are seldom met in the contemporary literature. Instead of widespread recipes of mathematical physics based on the solutions of integro-differential equations， we prefer logical and partly intuitional derivations of noncommutative algebra. The reader， having become armed with the necessary knowledge and skills from classical physics and symbolic mathematics， can thus directly penetrate the abstract world of quantum mechanics.
For exactly solvable models， we develop the method of factorization. This method， leaning primarily on Green's formalism， is applied for consideration of simple problems in the theory of vibrations and the relativistic theory of an electron. For more complicated problems， mainly related to the physics of various effects of anharmonicity， we develop the method of polynomials of quantum numbers， which enables one to systematize the calculations according to the perturbation theory. Regarding the quantum field theory and the calculation of observable radiative corrections， we rely entirely on Dirac's ideas， not on -at present-the pervasive rules of operation with a scattering matrix. Dirac's theory， possessing a proper elegance， is built on the equations of motion and is suitable for a first acquaintance with the principal problems of quantum electrodynamics， a matter of belief that remains open.
The author respectfully expresses his gratitude to John Ogilvie， who read the manuscript and made valuable comments. This book addresses a wide readership with serious enthusiasm about theoretical physics.
Quantum mechanics is one of the most fascinating， and at the same time most controversial， branches of contemporary science. Disputes have accompanied this science since its birth and have not ceased to this day. What is the sense of a probability interpretation of a physical phenomenon? Which approach to a quantum field theory is more consistent? How must we comprehend a quantum world? This book，leaving aside the search for spiritual content and answers to these questions， allows one to deeply contemplate some ideas and methods that are seldom met in the contemporary literature. Instead of widespread recipes of mathematical physics based on the solutions of integro-differential equations， we prefer logical and partly intuitional derivations of noncommutative algebra. The reader， having become armed with the necessary knowledge and skills from classical physics and symbolic mathematics， can thus directly penetrate the abstract world of quantum mechanics.
For exactly solvable models， we develop the method of factorization. This method， leaning primarily on Green's formalism， is applied for consideration of
simple problems in the theory of vibrations and the relativistic theory of an electron. For more complicated problems， mainly related to the physics of various effects of anharmonicity， we develop the method of polynomials of quantum numbers， which enables one to systematize the calculations according to the perturbation theory. Regarding the quantum field theory and the calculation of observable radiative corrections， we rely entirely on Dirac's ideas， not on -at present-the pervasive rules of operation with a scattering matrix. Dirac's theory， possessing a proper elegance， is built on the equations of motion and is suitable for a first acquaintance with the principal problems of quantum electrodynamics， a matter of belief that remains open.
The author respectfully expresses his gratitude to John Ogilvie， who read the manuscript and made valuable comments. This book addresses a wide readership
with serious enthusiasm about theoretical physics.
Preface
1 Ideas and principles
Quantum world
Probability waves
Physical operators
Noncommutative physics
Moment of momentum
Perturbation theory
Factorization
Oscillator
Quantum numbers
2 Physics of the electron
Hydrogen atom
Bohr's formula
Matrix elements
Dirac's equation
Relativistic invariance
Spin one—half
Pauli's theory
Elementary consequences
Useful definitions
Positrons
Fine structure
Solution according to factorization
Magnetic interaction
Landau levels
Anharmonicity
3 Theory of anharmonicity
Model Hamiltonian
Perturbation method
Inclusion of degenerate levels
Polynomial formalism
Ensemble of anharmonic oscillators
General equations
Physical interpretation
Rules for polynomials
Quantum functions
Other anharmonic models
Morse potential
Generalized Morse problem
4 Quantum fields
Creation and destruction operators
Free scalar field
Quantization of electromagnetic field
Fermi's ideology
Electron—positron Dirac field
Interaction picture
Solution according to perturbation theory
Normal product
Ultraviolet divergences
Regularization of interaction energy
5 Radiative corrections
Renormalization of mass
Anomalous magnetic moment of the electron
On the history of radiative corrections
Bethe's formula
Electromagnetic shift of atomic levels
Vacuum polarization
Renormalization of charge
Dirac's ideas and quantum field theory
Bibliography
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