11:13 X f f f · ° VOLTE Answered... ☐ : bartleby.com Q SEARCH Mechanics 14. **Dirac Equation** \[ ASK VX MAT (i\gamma^\mu \partial_\mu - m)\psi = 0 \] 15. **Klein-Gordon Equation (for scalar particles)** \[ (\partial^\mu \partial_\mu - m^2)\psi = 0 \] ### **Quantum Field Theory Basics** 16. **Path Integral Formulation** \[ \langle \phi_f| e^{-iHt}|\phi_i \rangle=\int e^{iS[\phi]/\hbar} D\phi \] 17. **Feynman Rules (Propagators, Interactions)** \[ G(x,y) = \int \frac{d^4p}{(2\pi)^4} \frac{e^{-ip(x-y)}}{p^2 - m^2 + i\epsilon} 11:13 X f f f · 응 Q SEARCH VOLTE Answered... о ☐ ☐ ⠀ bartleby.com ASK VX MAT 13. **Bose-Einstein Distribution** \[ 1} f(E) = \frac{1}{e^{(E - \mu)/kT} - \] ### **Relativistic Quantum Mechanics** 14. **Dirac Equation** \[ (i\gamma^\mu \partial_\mu - m)\psi = 0 \] 15. **Klein-Gordon Equation (for scalar particles)** \[ (\partial^\mu \partial_\mu - m^2)\psi = 0 ### **Quantum Field Theory Basics** 16. **Path Integral Formulation** \[ \langle \phi_f|e^{-iHt}|\phi_i \rangle = \int e^{iS[\phi]/\hbar} D\phi 17

11:13 X f f f · ° VOLTE Answered... ☐ : bartleby.com Q SEARCH Mechanics 14. Dirac Equation \[ ASK VX MAT (i\gamma^\mu \partial_\mu - m)\psi = 0 \] 15. Klein-Gordon Equation (for scalar particles) \[ (\partial^\mu \partial_\mu - m^2)\psi = 0 \] ### Quantum Field Theory Basics 16. Path Integral Formulation \[ \langle \phi_f| e^{-iHt}|\phi_i \rangle=\int e^{iS[\phi]/\hbar} D\phi \] 17. Feynman Rules (Propagators, Interactions) \[ G(x,y) = \int \frac{d^4p}{(2\pi)^4} \frac{e^{-ip(x-y)}}{p^2 - m^2 + i\epsilon} 11:13 X f f f · 응 Q SEARCH VOLTE Answered... о ☐ ☐ ⠀ bartleby.com ASK VX MAT 13. Bose-Einstein Distribution \[ 1} f(E) = \frac{1}{e^{(E - \mu)/kT} - \] ### Relativistic Quantum Mechanics 14. Dirac Equation \[ (i\gamma^\mu \partial_\mu - m)\psi = 0 \] 15. Klein-Gordon Equation (for scalar particles) \[ (\partial^\mu \partial_\mu - m^2)\psi = 0 ### Quantum Field Theory Basics 16. Path Integral Formulation \[ \langle \phi_f|e^{-iHt}|\phi_i \rangle = \int e^{iS[\phi]/\hbar} D\phi 17

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter11: Particle Physics And Cosmology

Section: Chapter Questions

Problem 67P: (a) Calculate the approximate age of the universe from the average value of the Hubble constant,...

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(a) Estimate the mass of the luminous matter in the known universe, given there are 1011 galaxies, each containing 1011 stars of average mass 1.5 times that of our Sun. (b) How many protons (the most abundant nuclide) are there in this mates? (c) Estimate the total number of particles in the observable universe by multiplying the answer to (b) by two, since there is an electron for each proton, and then by 109, since there are far more particles (such as photons and neutrinos) in space than in luminous matter.
Distinguish fermions and bosons using the concepts of indistiguishability and exchange symmetry.
What is critical temperature Tc? Do all materials have a critical temperature? Explain why or why not.
The peak intensity of the CMBR occurs at a wavelength of 1.1 mm. (a) What is the energy in eV at a 1.1mm photon? (b) There are approximately 109 photons for each massive particle in deep space. Calculate the energy of 109 such photons. (c) If the average massive particle in space has a mass half that of a proton, what energy would be created by convening its mass to enemy? (d) Does this imply that space is “matter dominated”? Explain briefly.
What is the Standard Model? Express your answer in terms of the four fundamental forces and exchange particles.
How can quarks, which are fermions, combine to form bosons? Why must an even number combine to form a boson? Give one example by stating the quark substructure of a boson.
To get an idea of how empty deep spam is on the average, perform the following calculations: (a) Find the volume our Sun would occupy if it had an average density equal to the critical density of thought necessary to halt the expansion of the universe. (b) Find the radius of a sphere of this volume in light years. (c) What would this radius be if the density were that of luminous matter, which is approximately 5% that of the critical density? (d) Compare the radius found in part (c) with me 4-ly average separation of stars in the aims of the Milky Way.
A virtual particle having an approximate mass of may be associated with the uni?cation of the strong and electroweak forces. For what length of time could this virtual particle exist (in temporary violation of the conservation of mass-energy as allowed by the Heisenberg uncertainty principle)?
If there is no observable edge to the universe, can we determine where its center of expansion is? Explain.
Draw a Feynman diagram to represents annihilation of an electron and position into a photon.
Suppose you are designing a proton decay experiment and you can detect 50 percent of the proton decays in a tank of water. (a) How many kilograms of water would you need to see one decay per month, assuming a lifetime of 1031 y? (b) How many cubic meters of water is this? (c) If the actual lifetime is 1033 y, how long would you have to wait on an average to see a single proton decay?
Nuclear-powered rockets were researched for some years before safety concerns became paramount. (a) What fraction of a rocket's mass would have to be destroyed to get it into a low Earth orbit, neglecting the decrease in gravity? (Assume an orbital altitude of 250 km, and calculate both the kinetic energy (classical) and the gravitational potential energy needed.) (b) If the ship has a mass of 1.00105 kg (100 tons), what total yield nuclear explosion in tons of TNT is needed?