- Title Pages
- Dedication
- PREFACE
- ACKNOWLEDGEMENTS
- COPYRIGHT PERMISSIONS
- 1 Elementary concepts of nuclear physics
- 2 Nuclear matter as a Fermi liquid
- 3 Independent particles and quasiparticles in finite nuclei
- 4 From the shell model to the compound nucleus
- 5 Shell effects and Strutinsky renormalization
- 6 Average collective motion of small amplitude
- 7 Transport theory of nuclear collective motion
- 8 The statistical model for the decay of excited nuclei
- 9 Pre-equilibrium reactions
- 10 Level densities and nuclear thermometry
- 11 Large-scale collective motion at finite thermal excitations
- 12 Dynamics of fission at finite temperature
- 13 Heavy-ion collisions at low energies
- 14 Giant dipole excitations
- 15 Metals and quantum wires
- 16 Metal clusters
- 17 Energy transfer to a system of independent fermions
- 18 Elements of reaction theory
- 19 Density operators and Wigner functions
- 20 The Hartree–Fock approximation
- 21 Transport equations for the one-body density
- 22 Nuclear thermostatics
- 23 Linear response theory
- 24 Functional integrals
- 25 Properties of Langevin and Fokker–Planck equations
- 26 Formal means
- 27 Natural units in nuclear physics
- REFERENCES
- Index

# Formal means

# Formal means

- Chapter:
- (p.589) 26 Formal means
- Source:
- The Physics of Warm Nuclei
- Author(s):
### Helmut Hofmann

- Publisher:
- Oxford University Press

This chapter elucidates various mathematical formulas. Based on expressions for Gaussian integrals in one and many dimensions, the methods of stationary phase and steepest descent are deduced, representations of the delta-function are given and applied to Fourier and Laplace transformations. For quantal operators, the Mori product is introduced and an important formula for the derivative of exponentials is shown. Elementary properties of spin and isospin are discussed; for fermions, the formalism of second quantization is produced.

*Keywords:*
Gaussian integrals, stationary phase, steepest descent, delta-function, Fourier transformation, Laplace transformation, Mori product, derivative of exponential operator, spin and isospin, second quantization

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- Title Pages
- Dedication
- PREFACE
- ACKNOWLEDGEMENTS
- COPYRIGHT PERMISSIONS
- 1 Elementary concepts of nuclear physics
- 2 Nuclear matter as a Fermi liquid
- 3 Independent particles and quasiparticles in finite nuclei
- 4 From the shell model to the compound nucleus
- 5 Shell effects and Strutinsky renormalization
- 6 Average collective motion of small amplitude
- 7 Transport theory of nuclear collective motion
- 8 The statistical model for the decay of excited nuclei
- 9 Pre-equilibrium reactions
- 10 Level densities and nuclear thermometry
- 11 Large-scale collective motion at finite thermal excitations
- 12 Dynamics of fission at finite temperature
- 13 Heavy-ion collisions at low energies
- 14 Giant dipole excitations
- 15 Metals and quantum wires
- 16 Metal clusters
- 17 Energy transfer to a system of independent fermions
- 18 Elements of reaction theory
- 19 Density operators and Wigner functions
- 20 The Hartree–Fock approximation
- 21 Transport equations for the one-body density
- 22 Nuclear thermostatics
- 23 Linear response theory
- 24 Functional integrals
- 25 Properties of Langevin and Fokker–Planck equations
- 26 Formal means
- 27 Natural units in nuclear physics
- REFERENCES
- Index