Book ordering information
My book on ``Quaternionic Quantum Mechanics and Quantum Fields'' was published by Oxford University Press in 1995. It can be ordered from: Oxford University Press, 2001 Evans Road, Cary NC 27513; phone for orders (919) 677-0977 ; the price is $75.
Current list of book errata
- Page 102. In Eq. (4.51a), "U_{ab}" should read "U_{ba}".
- Page 123. In Eq. (4.119c), inside the square bracket "|V_{\beta}|^2 x^2" should read "|V_{\beta}|^2 x^4".(Thanks to Dr. Jeffrey Hersh for spotting this.)
- Page 275. The following line was omitted at the top of the page: "The operators a_{\lambda}^{\dagger},a_{\lambda} are formally real with respect to the"...(Thanks to Dr. Horace Crater for spotting this.)
- Page 393. In note 14, an incomplete notation was used for the generator expansions; one should have "U_b=e^{\sum_B \theta_B^b \tilde G_B" and with corresponding modifications throughout the entire footnote; the final result of Eq. (12.73b) is not affected. A corrected discussion is given in paper 2. below.
- Page 498. In Eq. (14.1), "C" should be on the same line as "(1,I)".
- Page 539, In Eqs. (A.15a) through (A.16), a factor of \epsilon_A was inadvertently omitted, which takes the value 1 for A=0 and -1 for A=1,2,3. This has no effect on the conclusions. A corrected discussion is given in paper 1. below.
- Page 553. On the next to last line, B145 should read B415 , and on the last line, 332B should read B332 .
- Page 570, column 1, line 6 from bottom, "multiparticle case, 234-37" should be aligned with "passive" rather than being indented.
- Page 574, Harmonic oscillator should have a subcategory with a cross reference reading "forced, see Forced harmonic oscillator"
- Page 585, column 1, lines 14 and 15 should be indented so that they are
subcategories of line 13, "notation T in ....".
More recent publications on quaternionic quantum mechanics and noncommutative dynamics are:
- "Generalized Quantum Dynamics as Pre-Quantum Mechanics" (with Andrew C. Millard), IASSNS-HEP-95/66;available from the bulletin
board as hep-th/9508076; Nucl. Phys. B 473, 199 (1996)
Shows that the canonical
quantization rules can be deduced from generalized quantum dynamics if one
assumes there is a regime where statistical mechanical methods can be applied.
Extends the discussion of Secs. 13.5-7 of the book. A related paper (with
L. Horwitz), "Microcanonical Ensemble and Algebra of
Conserved
Generators for Generalized Quantum Dynamics ", is on the bulletin board
as hep-th/9606023; J. Math. Phys. 37, 5429 (1996) For an update on
the paper with Millard, see S. Adler and A. Kempf, "Corrections to the
Emergent Canonical Commutation Relations Arising in the Statistical
Mechanics of Matrix Models", hep-th/9709106, J. Math. Phys. 39,
5083 (1998).
Gauge fixing is discussed
in S. Adler, "Gauge fixing in the partition function for generalized
quantum dynamics", J. Math. Phys. 39, 1723 (1998). The extension
of rigid supersymmetry to GQD is given in S. Adler, "Poincar\'e supersymmetry representations over trace class non-commutative graded operator
algebras", Nucl. Phys. B 499, 569 (1997). See also ``The Matrix Model for M Theory as an Exemplar of Trace (or Generalized Quantum)
Dynamics'' , Phys. Lett. B407, 229 (1997). Possible relevance of GQD
to the cosmological constant problem is discussed in "A Strategy for a
Vanishing Cosmological Constant in the Presence of Scale Invariance Breaking", Gen. Rel. and Grav. 29, 1357 (1997). For a pedagogical account of Andrew Millard's thesis, and the thesis text, see Millard's home
page http://www-wilson.ucsd.edu/~acm/papers/index.html
****NEW**** The draft of a
book on the trace dynamics program has been put on the bulletin board:
``Statistical Dynamics of Global Unitary Invariant Matrix Models as
Pre-Quantum Mechanics'', hep-th/0206120.
This has been expanded and published as a book by Cambridge University
Press in Sept, 2004, with the title " Quantum Theory as an Emergent
Phenomenon" A current list of errata and addenda for this book
is as follows:
- After the book went to press, I learned from Pierre Hohenberg of a review by Tony Leggett that is relevant to the discussion of Chapter 6: "Testing the limits of quantum mechanics: motivation, state of play, prospect", A. J. Leggett, J. Phys.: Conden. Matter 14, R415 (2002).
- On pages 164 and 165, in the second lines of Eqs. (6.10b) and (6.10d), a factor of dt was omitted. This factor does appear in the first lines of the two equations. In the sentence immediately following Eq. (6.10d), ``spatially correlated'' should read ``spatially localized''.
- "Projective Group Representations in Quaternionic Hilbert Space",
IASSNS-HEP-96/02; available from the bulletin board as hep-th/9601047; J. Math.Phys. 37, 2352 (1996). This paper discusses the consequences
of the associativity condition for projective group representations in
quaternionic Hilbert space, and extends the discussion given in Sec. 4.3 of the book. A later paper by Andrew C. Millard and Terry Tao, Princeton University, ``On the Structure of Projective Group Representations in Quaternionic
Hilbert Space'', proves a structure theorem for quaternionic projective
representations, and shows that multi-central implies central in the connected
case; this paper will also appear in J. Math. Phys. A
subsequent paper by S. L. Adler, "Response to the Comment by G. Emch on
Projective Group Representations in Quaternionic Hilbert Space " is
available from the bulletin board as hep-th/9609012; J. Math. Phys. 37, 6586, 1996; see also the paper with G. Emch, "A rejoinder on
quaterionic projective representations", J. Math. Phys. 38, 4758 (1997). A paper " Coherent States in Quaternionic Quantum Mechanics ", by S. L. Adler and A. C. Millard, appears in J. Math. Phys. 38, 2117 (1997).
Also, a paper "Nonadiabatic Geometric Phase in Quaternionic Hilbert Space " by S. L. Adler and J. Anandan, has been submitted to the Foundations of
Physics issue dedicated to the 60th birthday of Prof. Larry Horwitz.
