The Landscape of Theoretical Physics: A Global View : From Point Particles to the Brane World and Beyond, in Search of a Unifying Principle

by Pavsic, Matej

• ISBN13: 9780792370062
• ISBN10: 0792370066
• Format: Hardcover
• Copyright: 2001-08-01
• Publisher: Kluwer Academic Pub

Summary

Attempts to provide a synthetic view of fundamental theoretical physics. Of interest to those who would like to explore how the 'Theoretical Physics of Everything' could possibly be formulated.

Table of Contents

Preface	xi
Acknowledgments	xiii
Introduction	xv
Part I Point Particles
The Spinless Point Particle	3	(50)
Point particles versus worldlines	3	(4)
Classical theory	7	(9)
First quantization	16	(15)
Flat spacetime	16	(4)
Curved spacetime	20	(11)
Second quantization	31	(22)
Classical field theory with invariant evolution parameter	31	(4)
The canonical quantization	35	(10)
Comparison with the conventional relativistic quantum field theory	45	(8)
Point Particles and Clifford Algebra	53	(40)
Introduction to geometric calculus based on Clifford algebra	54	(5)
Algebra of spacetime	59	(3)
Physical quantities as polyvectors	62	(7)
The unconstrained action from the polyvector action	69	(6)
Free particle	69	(4)
Particle in a fixed background field	73	(2)
Quantization of the polyvector action	75	(8)
On the second quantization of the polyvector action	83	(4)
Some further important consequences of Clifford algebra	87	(5)
Relativity of signature	87	(3)
Grassmann numbers from Clifford numbers	90	(2)
The polyvector action and De Witt-Rovelli material reference system	92	(1)
Harmonic Oscillator in Pseudo-Euclidean Space	93	(14)
The 2-dimensional pseudo-Euclidean harmonic oscillator	94	(2)
Harmonic oscillator in d-dimensional pseudo-Euclidean space	96	(3)
A system of scalar fields	99	(3)
Conclusion	102	(5)
Part II Extended Objects
General Principles of Membrane Kinematics and Dynamics	107	(38)
Membrane space M	108	(6)
Membrane dynamics	114	(24)
Membrane theory as a free fall in M-space	114	(12)
Membrane theory as a minimal surface in an embedding space	126	(4)
Membrane theory based on the geometric calculus in M-space	130	(8)
More about the interconnections among various membrane actions	138	(7)
More about Physics in M-Space	145	(22)
Gauge fields in M-space	146	(12)
General considerations	146	(1)
A specific case	147	(5)
M-space point of view again	152	(3)
A system of many membranes	155	(3)
Dynamical metric field in M-space	158	(9)
Metric of VN from the metric of M-space	163	(4)
Extended Objects and Clifford Algebra	167	(36)
Mathematical preliminaries	168	(12)
Vectors in curved spaces	168	(9)
Vectors in an infinite-dimensional space	177	(3)
Dynamical vector field in M-space	180	(8)
Description with the vector field in spacetime	183	(5)
Full covariance in the space of parameters φA	188	(15)
Description in spacetime	188	(7)
Description in M-space	195	(2)
Description in the enlarged M-space	197	(6)
Quantization	203	(46)
The quantum theory of unconstrained membranes	203	(20)
The commutation relations and the Heisenberg equations of motion	204	(1)
The Schrodinger representation	205	(5)
The stationary Schrodinger equation for a membrane	210	(1)
Dimensional reduction of the Schrodinger equation	211	(1)
A particular solution to the covariant Schrodinger equation	212	(5)
The wave packet	217	(3)
The expectation values	220	(2)
Conclusion	222	(1)
Clifford algebra and quantization	223	(26)
Phase space	223	(2)
Wave function as a polyvector	225	(4)
Equations of motion for basis vectors	229	(9)
Quantization of the p-brane: a geometric approach	238	(11)
Part III Brane World
Spacetime as a Membrane in a Higher-Dimensional Space	249	(22)
The brane in a curved embedding space	249	(7)
A system of many interesting branes	256	(5)
The brane interacting with itself	258	(2)
A system of many branes creates the bulk and its metric	260	(1)
The origin of matter in the brane world	261	(3)
Matter from the intersection of our brane with other branes	261	(1)
Matter from the intersection of our brane with itself	261	(3)
Comparison with the Randall-Sundrum model	264	(7)
The metric around a brane in a higher-dimensional bulk	267	(4)
The Einstein-Hilbert Action on the Brane as the Effective Action	271	(12)
The classical model	272	(2)
The quantum model	274	(7)
Conclusion	281	(2)
On the Resolution of Time Problem in Quantum Gravity	283	(20)
Space as a moving 3-dimensional membrane in VN	285	(2)
Spacetime as a moving 4-dimensional membrane in VN	287	(16)
General consideration	287	(2)
A physically interesting solution	289	(5)
Inclusion of sources	294	(9)
Part IV Beyond the Horizon
The Landscape of Theoretical Physics: A Global View	303	(12)
Nobody Really Understands Quantum Mechanics	315	(24)
The `I' intuitively understands quantum mechanics	318	(5)
Decoherence	323	(3)
On the problem of basis in the Everett interpretation	326	(2)
Brane world and brain world	328	(5)
Final discussion on quantum mechanics, and conclusion	333	(6)
Final Discussion	339	(8)
What is wrong with tachyons?	339	(1)
Is the electron indeed an event moving in spacetime?	340	(2)
Is our world indeed a single huge 4-dimensional membrane?	342	(1)
How many dimensions are there?	343	(1)
Will it ever be possible to find solutions to the classical and quantum brane equations of motion and make predictions?	344	(1)
Have we found a unifying principle?	345	(2)
Appendices	347	(6)
The dilatationally invariant system of units	347	(6)
References	353	(10)
Index	363